The Stupid Helmet

Eric's empathy is more selective, but he is a compassionate person.

The people named in your ask:

His mother (Kitty)

His girlfriend/fianceé/love of his life (Donna)

Jackie (inconsistent antagonist; consistent supporter of his relationship with Donna; his one-time hero vs. Laurie)

Mitch (consistent antagonist who reveals his vulnerability to Eric once, which Eric can relate to, only to be betrayed by Mitch as a result of showing him empathy).

Eric has a close, positive relationship with his mom and Donna.

By season 4, Jackie is no longer a stranger to Eric but someone he's witnessed -- and passively enabled -- harm being done to her by Kelso. By helping her with Kelso in S4, he's (likely subconsciously) making up for his inaction while Kelso cheated on her with his sister.

Mitch is Eric's nemesis, one who's pathologically jealous of what Eric has in family, friends, and girlfriend. When Mitch finally seems to capitulate by expressing what seems to drive his relentless antagonism toward Eric, Eric's compassion isn't fully altruistic. It's also self-serving. Finally, he believes -- as is evident from his dialogue and actions -- Mitch will leave him alone after a public truce. Mitch played him, of course, and used Eric's words of peace to mock him.

[Hyde] doesn't distinguish between friend or stranger, vulnerable antagonist or vulnerable father (Bud) who betrayed him but needs help paying the rent.

Jackie (consistent antagonist to boundary invader to girlfriend)

Eric (best friend since first grade)

Fez (stranger then friend)

Donna (very close friend since first grade)

Kelso (very close friend since first grade to antagonist)

Kitty (parental guardian)

Red (parental guardian)

Leo (boss to boss-friend to father/son figure)

Mitch (random classmate)

Caroline (virtual stranger; Fez's relatively new girlfriend)

Bud (the alcoholic [step]father who abandoned Hyde when Hyde was nine)

Kelso and Brooke's unborn baby (stranger)

Eric, Donna, Kelso, Kitty, Red, and Leo need little explanation. They're personal relationships.

Jackie is a complex case. They "kind of hate each other," he says to her in "Prom Night," yet he still helps her when they're antagonists.

In season 2, although his friendship loyalty is to Kelso, his personal moral code drives him to help Jackie catch Kelso cheating. He doesn't like her as a person; he states this fact directly in "Kelso's Serenade" (2x21). Yet he still supports her in the aftermath of her dumping Kelso. Once she starts idolizing him and invading his boundaries, he continues to protect her despite her unwelcome behavior.

Mitch: Hyde -- along with Eric and their guy friends -- make sure to get Mitch to the hospital after Eric's golf ball knocks Mitch unconscious.

Caroline is stuck at The Hub at night without a car. She's afraid to walk home. Hyde barely knows her, has no personal connection to her, but offers to drive her home and does. (To be fair, I think Eric would've done the same.)

Bud: Hyde chooses to moves in with Bud in "Hyde's Father" (3x03) and gives him money to cover his rent. Hyde knows full-well Bud is using him, but he helps Bud anyway despite the history of neglect and abuse because, as he tells Red, "He's my father." Hyde's childhood wounding is at work here. He puts his anger aside and helps the man who continues to abuse him as soon as they "reunite". (Recovering alcoholic Bud uses beer and a strip club to blunt Hyde's anger at him -- a lot of manipulation going on.)

Fez: Hyde, Eric, and Kelso first discover him stuck on a hook in a gym closet at school. He was put there by jocks. Kelso wants to abuse Fez further, which Hyde stops, and Eric is relatively passive about the situation. Hyde, though, lifts Fez off the hook. Hyde tells Fez to go to him if anyone bothers Fez again -- because Hyde will take care of the problem and protect Fez from more harassment. Hyde proves his word when Kelso begins bullying Fez verbally and tackles Kelso to the ground.

Kelso and Brooke's unborn baby: Hyde does not want another child to experience what he did while growing up. No father (while physically present in the home and after he left) and how his father's absence deeply affected his mother and her treatment of him.

The real core of my argument, however, that Hyde is more protective is the following (and your ask inspired me to think more deeply about my answer):

The consequences and cost to Eric showing compassion are far less dire than those to Hyde. Eric takes emotional risks, particularly with Red in season 5 and that one episode with Mitch. His most significant life-altering choice is delaying college after his father's heart attack. But it is a delay, not a full sacrifice (it would've been a much shorter delay had Red not spent Eric's college fund, which real!Red never would've done; plot manipulating character).

Hyde, in contrast, risks his physical safety and core emotional safety.

In "Prom Night" (1x19), Hyde spends what little money he has to give someone he actively dislikes (i.e. Jackie) as good an experience as possible at Prom while she's heartbroken. He hates dances, but Jackie's needs are more important to him than his discomfort. He dislikes dancing, but he dances with Jackie while trying to comfort her.

He spends much of season 1 trying to convince Kelso to dump Jackie because she's a disruptive presence in the basement, controlling, and abrasive. Yet in "Prom Night," Hyde puts what he wants aside because both Jackie, an antagonistic he feels compassion for, and one of his best friends are miserable apart. He reconciles them

In "The Good Son" (1x25), had Eric taken responsibility for breaking the living room TV, Red would not put him on the street. Her ground him and make him pay for a new television. Hyde, newly moved-in to the Forman home, could've been kicked out for such a transgression. As far as Hyde's concerned, he has no reason to think otherwise. Yet he takes the blame for Eric's actions out of gratitude and friendship and to protect Eric from non-existential consequences Hyde himself might face.

In "Cat Fight Club" (2x25), Hyde teaches Jackie one of his own self-protection techniques so she can stop being victimized by Laurie, who is also Kelso's proxy. By revealing to Jackie how he's protected himself for years, he also makes himself extremely vulnerable to Jackie. She can see through this vital defense of his. He sacrifices his own emotional safety, where she's concerned, so that she can have it herself. And she does use his personal, private knowledge to try to get what she wants from him in "Jackie Bags Hyde" (3x08).

In "Moon Over Point Place" (2x26), Hyde goes to jail in Jackie's stead. A boatload of concrete, potentially existential consequences in that choice to protect Jackie from likely less harm. Her father's a powerful, influential attorney, and I have no doubt he would've gotten the charges dropped and expunged from her record. Hyde has no one who can or is willing to help him in such a way.

The above leads to "Reefer Madness" (3x01), where Hyde continues to protect Jackie by keeping the truth to himself, despite Red kicking him out of the house. Had Donna not interceded, Hyde would've been homeless. Eric wanted to intercede before then, but Hyde rejected Eric's plan to protect him. No point in Forman getting in trouble, too, Hyde says.

Later in the episode, once Red learns the pot was Jackie's, Eric follows through on his plan anyway. He admits to smoking pot, too. The consequences for Hyde and Eric "trying" pot again, though, are far different in scale.

Red tells Hyde that if he ever finds that Hyde has pot / is smoking pot, he'll be kicked out of the house. That's the sword of Damocles dangling above Hyde's head. His safety isn't assured. Red has indirectly told him that Hyde isn't quite family. Living with that underlying fear and lack of unconditional love takes a huge emotional toll

Erc does not get that same threat. His safety and family security isn't in question.

Despite Red telling Hyde in "Hyde's Birthday" (4x23) that Hyde can stay in the Formans' home as long as he likes; no time limit, "Misty Mountain Hop" (5x12) demonstrates that this assurance is conditional. It also reaffirms that Hyde's not-quite family to Red. Red spots Kelso's bag of pot in Hyde's hands and kicks Hyde out of the house -- until Jackie steps in and protects Hyde's safety and future as he protected hers in "Moon Over Point Place".

Red is on the verge of crying when he tells Hyde he's "out of the house," but he makes the proclamation through his pain. Hyde isn't his child. Eric abd Laurie are. Kitty doesn't make that distinction. Red does; even if it's a small distinction, it's significant enough for him to exile Hyde.

Easier to choose compassion when one's life isn't at risk -- or feels at risk. Eric has enough experience confronting his father during S1-S4 to know his life won't be in danger. Yes, Red and Kitty both conspire to coerce Eric to end or delay his engagement to Donna. The worst is when Kitty sabotages his chance at getting a bank job to help pay for college. But Red and Kitty want Eric to go to college; that's ultimately why the engagement scares them. They're afraid Eric will forget about higher education if he and Donna get married as teens.

That storyline has a lot of holes in it, which is beyond the scope of this lengthy meta.

Choosing compassion when it means sacrificing money to pay for food, going to jail, being homeless is a lot tougher. This is why I say Hyde is more protective of others than Eric. He's consistently willing to negate his own wishes, needs, and safety to help people. And he consistently does so throughout the series, beginning in "Prom Night" (1x19).

Eric grows up in a stable family environment with parents who protect him, provide for him, love him.

Hyde grows up in a home with two alcoholic parents, an emotionally and physically abusive mother, a father who abandoned him at nine-year-old, a mother who leaves him alone regularly for days on end until she leaves for good when he's seventeen. Hyde is exposed to drugs, booze, gambling, and his mother's myriad lovers when he's a child. His cousins and uncles all ended up in prison, menial dead-end jobs, or dead.