I care a lot about character interactions and stuff. It's why whenever I come up with an MU, I try to come up with a good reason for them encountering each other, why they'd fight, how they'd interact, and possibly even how the fight would end, if they'd kill them, if they'd incap, accidentally kill, if they'd regret the kill, etc etc. I actually really like alternate methods of fights ending too, draws can be fun if well executed, and in certain fights not everyone has to die (something like Kasen Ibaraki vs Fleetway Sonic could end with Kasen BFRing and destroying Super Sonic's soul, but allowing Fleetway himself to survive, so someone still dies, but the characters can still reconsile in the end).
It's fun to not be so one-tracked in how things HAVE to go or whatever.