When they were very small (different marriage)? Me. No question.
Now they're teens (and up), second marriage? I do my kids, he does his, mostly. Not in any sort of unfriendly or resentful way, but because the children respond best to "their" parent. It's natural and easier that way.
Having said that, they're teens. They don't require the sort of hands-on parenting of small children. (Little kids have simple problems and need almost constant tending-to; teens tend to need only intermittent tending-to, but when they have problems, they're bigger and more intense! You win some, you lose some! I loved being a parent of wee ones, and now I'm really enjoying being a parent of teens!