Alistair will kill Loghain afterwards if he fights him during the Landsmeet duel.
You don't get out of landsmeet with both. Only one will remain in the game. You _may_ have one still in your party, you may not, depending on how landsmeet goes. Either may die. Either may be in your party. None may die. None may be in your party. But at least one will survive landsmeet, even if he isn't in your party.
Loghain is a champion and comes with his own armor and shield, (which isn't bad - strip alistar before landsmeet to keep his armor & weapons). Alistar is a templar. OTOH, you've had the whole game to develop Alistar any way you like, including whether he likes you, or is in love with you. There isn't enough time, (nor enough gifts), to get Loghain to like you much. And since you don't have much time to develop Loghain, you aren't likely to get him into, say, legion armor, (not enough strength).
Loghain makes for an interesting change of pace if you're bored of Alistair, though.
You need to get Loghain into your party eventually with some character if you want all of the achievements.
(Note: if you save game before landsmeet, then you can play it through several different ways, although some of the results depend on actions you've taken much earlier.)