I can only ever let Anora rule alone. Sometimes I’ll marry her to Alistair, but I never let Alistair rule alone. Anora has experience with ruling, is loved by the people and actually WANTS to rule, unlike Alistair. I just personally think Anora’s more suited to the job, though I can understand why others let Alistair be sole ruler.
I think both have their strengths and weaknesses. Anora is the better, more experienced leader of the two, but Alistair is beloved of the people and he tries to improve the lot of the elves (appointing the Alienage Elder to his court, not to mention the elven riots and resulting crackdown not happening when he’s king).