i can't say there's any one thing that can draw me to music, but generally a combination of things. i believe there's lots of things that can be the dominant factor from any one band, but good bands usually have 2 or more.
ideally, i like bands that are a total package, but those are hard to come by.
i'm not overly snobby with a band having to be great live, but i rarely like bands that suck ass live. with certain genres, i let it slide more than others. i would rather see a band that is a little sloppy live that keeps my "indie rock head nod" goin than a band that plays perfectly, effortlessly, and heartlessly
when you have a psycho memory like i do, i always find that bands have a lot of sound going on to be more interesting since i cannot "play it back" in my head from memory and still get all of the parts at once.
i also tend to get drawn to contrasts and etremities. i.e. if it doesn't rock it better be so pretty your heart bleeds until you vomit blood.
i'm not too concerned with a singer's voice unless it is particularly good or particularly bad. i focus more on the effort they put into it and whether or not they wear their heart on their sleeve.
lyrics can make or break a song to me. lyrics were able to get me liking a style of music that i didn't like before. imo, some of the best lyrics from the past decade were from the band Saetia, who had extremely heavy screaming in the song. the lyrics were so good it got me to enjoy a good hardcore screamer.