For me, Final Fight (Arcade) is the best game of either that series or Streets of Rage. The following is all IMO, of course.
Haggar is by far and away the most interesting protagonist to play with.
The basic attack in Streets of Rage 1 and 2 (I haven't played 3 very much) just seemed to lack much oomph (feeling of impact). I put that down to the disappointing sound effect, which admittedly was improved in SoR2 over SoR. In Final Fight there's a much more satisfying smack sound when you connect. It's surprising how much difference that makes.
The enemies are better in Final Fight, and certainly more iconic. It always looked a bit strange to me that the knife enemy in SoR just walked towards you holding out. I much preferred El Gado and Holly Wood in Final Fight who would throw them at you (and you could pick them up if they missed), as well as their jumping knife attack. Plus, they don't do this:
The range of enemy attacks in Final Fight is excellent. Some will try to get behind you, some will jab once and then hop back out of range (Two-P), some will stand off and jump over your punch (Roy / Poison), some will wait and charge (Andore, I hate you) and some will just come forwards. Some of the bosses in SoR one are infuriating. They're better in SoR 2 although Velhelits, whatever it was supposed to be, I always found lame.
The music is better in SoR, certainly.
I'd say that the SoR trilogy is better overall than the FF trilogy, especially if you take the SNES versions of Final Fight One. But the best game for me is Final Fight One arcade version.
I enjoyed Mighty Final Fight and Streets of Rage 4. Final Fight Revenge was poor, and Streetwise is a shitstain that should have lead to imprisonment.