Eye of the beholder

Both men don't like to express themselves emotionally. It really does take more extreme circumstances to get them to voice their actual emotions. In my fics, they've known each other for long enough and are more open/honest than canon Yu Junghyeok and Kim Dokja would be.

Yu Junghyeok canonically struggles with confrontation (as in, the verbal kind/fighting between friends and allies, not fighting enemies) and isn't good at navigating them. So, he comes off as stiff and blunt. He has a very mechanical way of thinking, and he doesn't actually express everything he wants to say in words. That's why I usually write Kim Dokja reading between the lines and responding to what he's actually wanting to say rather than what he's really saying (unless he's purposefully doing it just to be a brat). This way of speaking usually causes misunderstandings and discomfort in the people around him, since he's not polite about what he says and has a rough way of speaking. But those who get to know him (like KimCom and especially Kim Dokja, who is fine-tuned to Yu Junghyeokese, even if he doesn't always understand Yu Junghyeok's feelings) come to interpret what he's saying.

He's also, straight up, a tsundere. As in, he's not honest and will say stuff that will on the surface mean one thing but he's actually saying another. This is stuff that Kim Dokja usually willfully misunderstands in his "Yu Junghyeok is a psychopath and can't possibly care about me" way. Some examples from canon (somewhat paraphrased):

Yu Junghyeok shows upset about Kim Dokja's death after the Nirvana fight. We saw proof he was worried he wouldn't wake up when he rescues Yu Sangah (though Kim Dokja interpreted it differently. Ignore his unreliable narrator). Then when they meet again in the Banquet, Yu Junghyeok says:

"When will you revive? The others are worried." What he actually means is that he was worried, but he's using other people as a shield. You'll notice from the fic I used this method a few times (Yu Junghyeok using Yu Mia as an excuse "Yu Mia misses you" rather than "We miss you"), but he does it in canon too.

Another tsundere moment is with the Skybreaking Sword Saint (the only person other than Kim Dokja who knows Yu Junghyeok very well and is close to him) being like "Is that your friend?" (about Kim Dokja) and Yu Junghyeok, embarrassed, being like "No, we're not", but since the scene is from SBSS's POV, the narration exposes how she saw through his lie by saying "She looked at her disciple's friend".

So basically, yeah, Yu Junghyeok is blunt and dishonest. He's more likely to show this cute dishonest side to people he cares about. He does it during the Lee Seolhwa scene talking about the Moisturization skill too.

Kim Dokja is harder. He also lies, but he does it in a way that's usually misleading. He'll acknowledge an emotional conversation (or one that touches on a subject he doesn't want to talk about), but will typically try to steer it away by dismissing the first topic. One example is with Jeong Huiwon hearing him say "Mother" in his sleep. Internally he's like "No way, did I really do that?" but out loud he just dismisses it by saying "Well, even I worry about people. More importantly-" and changes the subject. Usually, he's good about this. But depending on how stubborn the person he's talking to is (usually Yu Junghyeok, but Han Suyeong to some extent too. She typically allows him to change the topic, but in a way that tells us she's well aware of what he's doing and why, while Yu Junghyeok will force the conversation back to the previous topic if he isn't done yet or doesn't want to follow Kim Dokja's convo direction), he'll have to try a few ways to dodge the topic. He's someone who gets uncomfortable when things get too emotional, but unlike Yu Junghyeok, he's more willing to have heart-to-hearts (when it's about another person, rather than him). And when he does have emotional talks about himself, it's going to be in private one-on-one situations. If he feels he's being too raw, he'll try to backtrack, but other times he'll actually just live in the moment. It really depends on the mood of the conversation.

Kim Dokja also likes teasing people. He likes joking around, but his jokes tend to be awkward. In canon, Kim Dokja's jokes are lame, and Yu Sangah is pretty much the only one who genuinely finds them funny (and will go along with them). However, Kim Dokja and Jeong Huiwon have a great buddy-buddy teasing dynamic where they will mess with each other (though Jeong Huiwon is usually the one who starts it). Kim Dokja is more likely to tease/bully teenagers and Yu Junghyeok. So, most of his teasing will be directed toward them. He has a distinctly more casual and familiar way of messing with Yu Junghyeok at every point in ORV (which is why YJH calls him out on it in the beginning). Picture how you would mess with good friends you have known for a while vs how you would tease people you're friendly with but you're not comfortable enough they understand your humor to be completely at ease around them. That's the difference between how KDJ teases YJH vs others.

Yu Junghyeok and Kim Dokja are also so petty. Like, they're not ones to let an offense slide, especially in regards to one another. They always like to even the scales. They are also both likely to think "Yu Junghyeok/Kim Dokja would never let me live this down if he found out" because they're both correct. Yu Junghyeok won't bring it up as much, but he'll use Kim Dokja's silly screw ups against him, and Kim Dokja will 1000% tease Yu Junghyeok if he saw something funny. That's actually one of the primary reasons Yu Junghyeok did NOT want Kim Dokja finding out about his Punisher form because he fully expected Kim Dokja would mess with him about it. And both of them are too prideful to wanna suck that up.

Kim Dokja is actually pretty good at navigating social situations. He's not really awkward, but rather, trapped by polite conventions (such as when he's talking to superiors or coworkers) and his inherent disinterest in wanting to engage. Depending on his level of affection, he'll be anywhere from friendly to polite conversation to outright rude. He's more likely to be rude around those he has a grudge against, but it's situational. He has enough ability to recognize Time and Place to know when he has the power to be as audacious as he truly is. He normally doesn't try to stir the pot when it can fuck him over, but sometimes he just can't help himself.

Yu Junghyeok, on the other hand, bulldozes his way through. He canonically doesn't really understand the inner thoughts of people or normal social conventions. He grasps some of it enough to know when to respond or be polite (at least, pre-scenarios) but normally doesn't bother because the end result doesn't really change. He'll say what he wants when he wants it, but he's not one to talk all that much to begin with. That's why Kim Dokja often says that Yu Junghyeok manages to shoot himself in the foot with his arrogance (which canonically resulted in even the SBSS beating him to death in the 8th turn for it). Don't expect Yu Junghyeok to have social grace. His specialty lies on the battlefield.

Kim Dokja also is very attentive to those around him. He doesn't say so much in the narration of ORV, but we get multiple times where he talks about others (for example, his conversation with Jeong Huiwon about the Jeong Huiwon he knows) that tells us he pays close attention to them. He's excellent at reading people, and he listens very well. This is why KimCom like him so much. He can come off as dismissive, but he cares very deeply. He's empathetic and kinder than he says he is, and he's someone who, once he learns their story, will come to sympathize with them even when they're an enemy. He holds grudges, but if he sees someone is genuinely repentant, he's usually quick to start to let go of that grudge (as opposed to Yu Junghyeok who will literally hold that grudge forever in a "I can forgive but never forget" kind of way. Though, whether or not he forgives at all depends on the offense. He STILL holds grudges against Han Suyeong even up through the epilogues). For example, both Iris and Kim Namwoon are characters he explicitly says he hated (and he shows as much). But he forgives Kim Namwoon in the Underworld, and he helps Iris during the Gourmet Association (more to spite Anna Croft and to help Selena Kim, who he actually likes, but also because Iris is a child and he's kinder to children), though he puts up a firm boundary between his assistance and his actual kindness. He is in no way kind to Iris in that scene, which is his resentment.

As for the dynamic between Joongdok (generally)

Both of them give the other more grace when they're being annoying. They'll bicker, but it's typically just their way of communicating. There's a lot of "Yu Junghyeok says one thing, but Kim Dokja can read between the lines and respond to that" going on. He understands that Yu Junghyeok isn't good at expressing himself but understands him well enough to know what he actually wants to say...except when he's being willfully blind (which is normally in canonverse because his knowledge of TWSA genuinely holds him back from reading Yu Junghyeok as an actual person who is dynamic and changes with interaction vs the stagnant factual characterization he knows from TWSA). Kim Dokja can and does get angry with Yu Junghyeok, but he has a major soft spot for him and forgives very quickly. He's very protective of him in a "Hey, NOBODY is allowed to mess with him EXCEPT ME!" kind of way (unless it's people he's good with, in which case, they're welcome to tease him). When he's just friends, he acts like he's aloof about his feelings toward Yu Junghyeok when it's talked about with others, but he's always the first one to get offended and riled up on Yu Junghyeok's behalf.

For Yu Junghyeok, he's not someone who will defend Kim Dokja verbally, but physically. He's an action-over-words kind of guy, and this goes for any of his relationships. This also includes when he's in a romantic relationship. He struggles with words, so he would rather just take direct action.

Romantically, I personally see Kim Dokja as having brat behavior toward Yu Junghyeok. He's likes to tease and be flirty, purposefully flustering Yu Junghyeok (who doesn't show it, but his silences or his frustrated "Shut ups" are what tell Kim Dokja he won this one). And he will have this push-pull dynamic with Yu Junghyeok, bantering in almost a comedic way (though usually with Kim Dokja leading and Yu Junghyeok giving shorter answers). Kim Dokja normally leads every conversation no matter who starts it, so keep in mind the intent of the conversation and have Kim Dokja lead it there. If it's meant to lead to kissing, direct it toward flirting. If Kim Dokja doesn't want a conversation to go a particular way, have him purposefully steer it off course. If he's trying to manipulate, have him twist words and act like a con artist. And if Yu Junghyeok wants to go along with it or not will decide how their actual conversation goes, though Kim Dokja normally will get the last word in no matter what.

Honestly, whether it's dokjoong or joongdok, Kim Dokja will verbally take the lead in any situation, except when actions speak louder. Then, Yu Junghyeok is the one who normally leads (in my opinion. Dokjoongs have their own dynamics for them I don't necessarily agree with, but that's why I'm a joongdok main).

Overall, both men are very private. I don't see either of them enjoying any PDA whatsoever. If they're going to be affectionate in public, it will be very subtle or done more through their energy and vibes together rather than physical intimacy or verbal stuff. But in private is where they both become more relaxed. I see them both as enjoying physical affection (though they would never say it) and they give gifts to show their love (since both struggle to be honest). Kim Dokja canonically likes giving gifts to those he cares about when he can afford it (and doesn't want to be stingy. Just look at how he gave Han Suyeong a bunch of coins for her to go shopping with the kids and Lee Hyeonseong in the Context of Constellations, and how he bought a sword and fancy new fits for himself and Jeong Huiwon). And Yu Junghyeok will give practical gifts that usually show he's paying attention to what the people around him need or want (which is why in my story he "randomly gifted" Kim Dokja a reading chair that Kim Dokja fell in love with).

I have a personal headcanon that Yu Junghyeok, when he feels very comfortable, gets very clingy in his sleep. So, I always have that. But I think it's funny for the two to argue about who is "the cuddler" when both of them are physically affectionate in private. It's just that they refuse to acknowledge their own clinginess and instead blame it on the other.