Ease of button input. SSF IV was a nightmare for me just because of that. A lot of people had an advantage over me because I wasn't fast or accurate enough to execute the most complex moves. Charge moves? Spinning circle moves? Even the less complex moves were impossible for me to input them under pressure. Tekken is a bit more forgiving on the inputs. They are lengthier, but easier to remember and execute.
On top of that, the game needs to be easy to pick up and hard to master. Something that SSF IV isn't. You either became good after losing 300 times or you didn't. You basically get thrown at the wolves if you go online.
Character design is probably the least important to many, but if a game looks too 2D'ish, I'll probably ignore it completely. Alternate costumes and outfits are a must for me. This is why I preferred DOA 5 Ultimate over the rest. Tekken Tag Tournament 2 decided to be extremely lazy with the alternate costumes in quantity and look; they were worse from the much superior Tekken 6.
Story isn't definitely the fighting genre's strength, but many of the games haven't even tried to get a decent story, so it isn't worth choosing a fighting game for the story. Mortal Kombat being an exception for this.







