I thought Sasuke wanted to surpass his brother for what he assumed he did. Similar to how Bakugo wants to surpass All might. Sasuke just comes with an extra layer of revenge.
Sasuke did want to surpass his brother and kill him, but after that he wasn't really sure what to do. It's not really the same as Bakugo wanting to surpass All Might for several reasons.
1) All Might didn't murder a bunch of people close to Bakugo.
2) Bakugo and All Might are not related.
3) Bakugo wants to become stronger than All Might, but not at the cost of leaving U.A. High, where on the other hand Sasuke left the village and became a villain or at least not one of the good guys in order to become stronger.
Also, I didn't mention this in my last post, but with Midoriya saving Bakugo in season one, it comes full circle in season six, whereas Sasuke would never go out of his way to save Naruto, at least not while they were at each other's throats, lol.
And despite Bakugo finding out Midoriya's secret, it didn't make him leave or turn into a villain. From then on in the series he actually wanted to protect Midoriya by getting stronger, but also not be outdone by him.
I can think of about 10+ more ways the relationships are not the same, but I think I'll just leave it at that.