I do think it's kind of funny how Teach is just, the exact opposite of Rocks in every way. It's clear that Teach respects (the image) of his late father, but despite that he is worse than him in almost every way. Which makes it even more wild that he is somehow finding more success in achieving his goals than Rocks did!
The most obvious example of this is how their respective crews perceive them. Rocks acquired strong crewmates by winning them in Davy Back Fights. While the Rocks Pirates were strong and got along casually, they weren't really a unified group.
They were willing to work with Rocks because it would help them achieve their own individual goals.
Now compare that to the Blackbeard Pirates:
Teach kind of has a cult surrounding him. While his crew may not "like" him and has no qualms calling him out when he does something stupid, they are also undoubtedly loyal to him. They believe in whatever Teach's plans for "The World" are, and are willing to put up with him for the sake of that shared ambition.
The Rock's Pirates were individuals first and foremost, and that's ultimately what did them in on God Valley. None of them cared about the fate of the Davy clan or what was going on behind the scenes in the World Government. They were just there for Treasure and Shakky.
Also with the Blackbeard Pirate's, half of the Titanic Captains had to fight to the death to earn their spot on his crew.
While Rocks bolstered his ranks by defeating strong people, Teach found people who were strong but also desperate. He deliberately chose the lowest level of Impel Down, where he could prove his strength to the criminals there by breaking into the prison and surviving, and also find people who weren't going to complain about going with him. He was able to garner respect from some of the most dangerous people in the world without lifting a finger. (Also I just realized Teach has a full set of teeth in this panel lol)
And this isn't the only instance of Teach utilizing psychology to get what he wants. In fact, he is very charismatic in a fucked up kind of way. It's how he nabbed Kuzan after all.
He wasn't forcing Kuzan to join his crew (though I'm sure the fact that Teach would probably try to kill Kuzan if he refused was a fact not lost on him), he instead had a "heart to heart" with the former admiral and it seems to have payed off!
Now compare that with how Rocks talks to Harald:
While the relationship between these two is different than Teach and Kuzan, Teach and Rocks were both recruiting two men with ties to the World Government. While Rocks is absolutely correct in his assessment of how the World Government views the giants, he also isn't very great at conveying that information to Harald in a way that isn't pushy and condescending.
Teach was willing to "humble himself" (I'm using quotes here because I doubt Teach is being sincere in half of the things he says) in order to appeal to Kuzan's emotions. He strategically reminded Kuzan that he's at ideological odds with the Navy in between apologizing for his crew's actions and telling him that he's free to take whatever path he wishes. It was probably manipulative on Teach's part but it worked!
Rocks on the other hand truly cared about Harald's well being, but couldn't take a step back to try and see things from Harald's perspective. While the government does only view the giants as potential soldiers to strengthen their military, Harald is also correct in saying that the giants will also be further ostracized from the rest of the world if they officially associate themselves with the Rock's Pirates. It's a delicate balance, and Rocks can't calm himself down enough to try and understand it.
I think herein lies the core difference between Teach and Rocks. Rocks was a very strong but also a very emotional man. He did have ambition, but the connections he had with others (Harald and Eris) ultimately took priority over defeating Imu. If Rocks was a worse man, I'm confident he probably would have made it closer to usurping Imu. The proof for this statement is Teach himself.
Teach is just a crueler version of Rocks. He's powerful and ambitious, just like his father, but he does not have the same code of honor. Where as Rocks threatened to kick Kaido's ass just for SUGGESTING he make Harald join his crew by force, Teach betrayed the man who took him in as a child without a second thought. He murdered one of his "friends" in cold blood, for something that Thatch might have just given him if Teach had asked.
Teach was able to accomplish more in just two years than Rocks had in his entire pirating career by completely forsaking friendship.
And yet, when Teach inevitably kicks the bucket, who's going to mourn him?
Rocks was a feared pirate, but he also had people who loved him. Harald and Loki felt immense grief after his passing, Garp and Roger felt bad for him to some extent, Eris was of course devastated, and Teach admired his deceased dad enough to name his ship after him. Rocks legacy as a pirate may have been scrubbed from history, but the bonds he had made ensured he left an impact on the world that could never be erased.
Teach's legacy obviously can't be erased at this point, he's become far too infamous across the world to ever be truly forgotten. But if he's ever in a dire situation, one where there's no hope of survival, is anyone going to care enough to comfort him? Will there be someone to soothe his aching heart like Garp and Roger did for Rocks?
Maybe Teach truly doesn't care about sentimental things like that. After all, he's not like his father.