The character definitely. Gender doesn't play a huge role in what I plan on doing. I'm far more into the 'story' of Dragon Age than the actual combat. That said, I am a heterosexual female and prefer to play ladies romancing the guys.
In Origins, I loved Alistair far too much for any females to slip past Ostagar without total fangirl squeeing and falling hard. So to romance Leliana I had to make a male character. While I loved Zev and Morrigan, it was only as friends. I found their personalities (which were fantastic fun) didn't mesh well with mine in a romantic capacity. Not romancing them actually made them deeper to me, since I did try, but didn't like the romantic dialogues much. Morrigan is particularly touching when, after gathering the book from Flemeth she asks if there is anything more there could have been and you tell her "I like you but as a friend only". Her response almost made me cry knowing what will happen later.
For DA2, none of the male options appealed to me. My first character (blindly going in) didn't recruit Fenris, didn't like Anders and Sebastian, while fun to flirt with was boring and poorly integrated as a romance. So she was my "Forever alone" Hawke. On subsequent plays I romanced all but Anders with males, females (did my first s/s romances in this game). Ultimately, my favorite was Isabela because of the depth of character development that comes from that romance. This was on Kit, my snarky rogue ladyhawke.
So tally:
Neria Surana, romanced Alistair: Heterosexual
Kit Hawke, romanced Isabela: Lesbian
I have yet to determine who will be my favorite companion (BTW in DA2, it was Varric who is completely unromanceable), some candidates are really jumping up to wave at me already. Strong contender is Dorian who utterly fascinates me and I will definitely be making a hot male Inquisitor for him. But what my favorite inquisitor will be and who they end with remains to be seen.
So to make a long post short (I know, too late) I don't care from gender. If an NPC interests me, that's the criteria.