I caught them all and yes this includes getting the Moltres by going to Sevii Islands in the main game. And I even used them when facing the E4 since it's for the sake of nostalgia like what I did for the original Red yeah I'm a cheater.
For this generation, I love these birds equally since although Zapdos and Articuno were my favorites for Gen 1, Moltres got a very good moveset compared with Gen 1: Flamethrower and Heat Wave which are enough to give Moltres a good moveset compared with Gen 1.
Do I think they're the best trio? That one I don't know since I haven't caught the other trio in other generations but so far the original legendary birds are tied with the legendary beasts in Gen 2 for me.