Streets of Rage 2 vs 1.
Sega must have paid off game mags in 1990 because aside from the music, SoR 1 sucked. Shit graphics, horrible scratchy voices, repetitive gameplay, enemies and hardly any move sets. Yet eveyr mag gave SoR 1 9s and 10s reviews.
SoR 2 at 16 megs (SoR 1 was I think 4 megs?) was amazing. My bro was big into PC games and it's obvious Genesis was better at arcadey fast paced games at the time, but he never made anything out of it, since he preferred slower paced PC games. But when he saw SoR 2 his eyes popped out and even said something like "why can't my computer do that?"
I know I'm in the minority but I much prefer Streets of Rage 1 over 2.
The characters are smaller in the first, which I don't think is a bad thing. You can fit more enemies on screen and there's a bigger "chessboard" for strategic gameplay as a result.
Every song of SoR is unique and memorable, SoR2 has "Go Straight" and everything past that sounds like a downmix. Dreamer was fire though.
The bosses of 1 were better thought out, the strategy to each was different.
The OP didn't specify if the jump in quality meant gameplay or graphics, but SoR2 stole the show in graphics, sure, but it seemed like it sacrificed everything else.