My Warden always fights Loghain. That way the Landsmeet power stays in my hands where it belongs. Hey, throughout the entire game everyone expects me to take care of everything, so why relinquish power when it's really useful? My current character snarks at people every time they ask her to find their "Lost Bag of Holding" or their mother's favorite bowl or to rescue their foolish friend/relative from some idiotic situation they have gotten themselves into. I always do the quests because I'm a completionist, but I love it when someone wonders if they can ask me to do some menial task, and I get to say something along the lines of, "Why not? Everyone else does."
As for who executes Loghain (assuming I don't make him a Warden, which doesn't happen very often), it depends on whether or not Alistair is hardened, whose marriage I'm arranging, and my current mood. However, 99 percent of the time I'm still the one that gives him the fatal neck chop unless I'm playing a male Cousland who wants to be king. That's about the only time I don't behead Loghain myself (and I make sure to keep Alistair unhardened, so he doesn't go off and assume the throne automatically).