My DD, who just turned 4, is pretty much a Daddy's Girl, and prefers he put her to bed. This consists of reading a few books, talking quietly about the next day, and laying with her for a while until she starts to fall asleep (it's getting better, we are soon hoping to just turn the light off and leave her, not quite there yet).
The problem is, it puts a lot of stress on DH when he has to do this every night. She will let me do it if he's out of the house at a meeting or whatever, but if he's in the house, she wants him. I am fine with this, as it gives me time to relax and take a bath or whatever, but DH is starting to resent it - the whole bedtime process can take up to 45 minutes or more. Last night she had a screaming fest when she wanted him to put her to bed, as it was my turn to do it. He ended up doing it:)
I guess I'm not sure if this is a battle that should be fought, except that my DH wants me to be able to share in the bedtime duties (I put DS to bed, but that's super easy, you just put him in his crib and he goes to sleep, ha!). If it were switched, I wouldn't mind putting DD to bed each night. I like to snuggle with her, she's getting so big, and I like it when I get to do it!
DD is super stubborn and fights most issues tooth and nail. We've tried charts and sticker charts and rewards and everything else under the sun. Also, it's very hard to pick a battle with a 4 year old who doesn't nap anymore, at bedtime. We try to prepare her in the morning by saying tonight is Mommy's turn to put you to bed, etc., and she's fine with it, until 7:30 rolls around.