If given the option to play either series, I would play Fatal Fury. I respect Street Fighter for what it is and acknowledge SFII for being the overall better package, but I never quite got into Street Fighter like I did SNK games.
On the Genesis I had Street Fighter II and Fatal Fury 2. SFII was a revelation. It was so great to finally have that game on the Genesis, as my friends had been playing it on the SNES for the longest time. However when Fatal Fury 2 came out, I ended up playing that way more than SFII.
There were things in FF2 that were simply incredible. The dual planes concept really added to the gameplay. Also, the interactive stages like when fighting Axel Hawk, how you can knock him back onto the electric ropes.
I actually feel the Genesis version of FF2 mirrored the faster smoother gameplay we have come to expect from modern fighting games more so than many games at the time. Fatal Fury 2 on AES looks incredible, but has more drawn out animations, and the jumps between planes are slower. On the Genesis (maybe due to the dropped frames of animation) the gameplay is snappier, and hard punches/kicks don't linger as long like they do on AES. This contributed to a faster more cohesive rhythm, which is possibly why I played it so much over Street Fighter II.