You can't really compare ESF to Budokai 2.
However, they share some of the same flaws..
The thing that really made the Budokai games not good fighting games, were "Stock Moves." Every character was pretty much the same, except for the way the moves looked, and the cutscenes played.
Punch Punch Punch Energy.. Punch Punch Kick Kick Kick.. The majority of the characters had the exact same moves, they didn't even bother creating unique animations for everybody.
Having lots of characters is great, but not if they're not unique.
ESF suffers from this too, when it comes to Advanced Melee. Personally, I think each character should have different combo strings, not just universal ones.
Sure, with 2 people you can have "lengthy" battles in Budokai2--but as Phatsluggah said, they're crappy ones.
Soul Calibur for instance, with use of the repel and parry system, created skillful battles, though if one person wasn't as good, it would definitely show (as it should.) (As a sidenote, I preferred SC1 to SC2.)
Anyway..
Budokai has by far better graphics, but by far worse gameplay..
On overall 'fun' rating, I'd have to pick ESF.