Who’s his biggest rival current day?
If it needs to match-up between them, Teach and Luffy, Shanks and Buggy (includes Buggy+Mihawk combined).
Its possible that the purpose of Buggy's fake Emperor position and giving Mihawk (former opponent of Shanks) under Buggy's command is creating a new Emperor rival to Shanks. Buggy owned Shanks's opponent Mihawk, so both could combined go against Shanks.
And notice that how Shanks's influence was also the reason in Buggy's rise since the time skip, they always talk about Buggy's relationship with Shanks.
We just see Buggy being mad at Shanks and wants to find One Piece because of him.
-Buggy is after Shanks, because Shanks is ahead of him
-Shanks is after Teach, because Teach is ahead of him
-Teach was after Main character before time skip, and then went after Main character's Wano alliance as well
So it might be like Buggy/Mihawk falls first, Shanks falls second, Teach falls EoS last.