Oh, many things! It all depends on the anime I'm watching, since the fighting scenes might be better in anime A, but the depth better in anime B. Ultimately, what I think is the reason as for watching it at all though, would be for entertainment, in which many parameters are important.
Character design, choreography, music(when it comes to anime), all of it!
Character design, choreography, music(when it comes to anime), all of it!