My first one, I had them rule together. For about five seconds. Then Alistair guilt-tripped me, so I reloaded a save and had Anora do it by herself. This was also due to the fact that I broke Alistair's heart because he was my romance option at the time. On another run, I had them get married while Alistair was still himself (not hardened) and was able to convince him to calm down. So he didn't guilt trip me, and I was with Leliana anyway, and the kingdom seemed to do fine. Then, I had Alistair rule by himself and lock Anora away. I felt bad for her, so I redid that. Basically, I like having Anora run the country.
I agonized over that decision almost as much as I did over who would rule the dwarves. The implications, both in the game and after you beat it, sound like they will affect tons of things in Dragon Age II. And, for that matter, Dragon Age III. I still have trouble choosing who should rule the dwarves.
And then Dragon Age II came out and I was shown that NONE OF IT MATTERED! Thank you so much for that. Ugh.