Legendary Birds, although I've very frustrating memories of catching them back in Yellow. Other than them the Lake Guardians are the only other full trio I bothered to catch.
Kyogre/Groudon/Rayquaza, always been a fave of mine since they showed up in Gen 3. Their shiny colours are the best, especially in their new forms introduced in ORAS.
My favorite trio is a bit of a toss-up. The legendary birds, beasts, and titans are all in contention. I'm a big fan of birds in real life, love Articuno and the idea of a phoenix Pok?mon in Moltres, though I flip-flop on its design, and am so-so in my opinion on Zapdos. I like all three beasts and all three titans without much to complain about.
As it stands today, I'd probably say:
1) Legendary Birds
2) Legendary Titans
3) Legendary Beasts
4) Weather Trio
5) Lake Guardians
6) Aura Trio
7) Tao Trio
8) Creation Trio
9) Forces of Nature
The birds and titans are on pretty equal footing and it sort of depends on the day which I prefer. I decided on 3rd place for the beasts because my affection for birds is too strong and I had to make a compromise somewhere to get the list in order. But yeah, right now I'll give it to the birds.
I would say the Legendary Birds, as I like them the most out of all trios. Especially because of their looks, I really like Articuno for example because of it's elegant design and the blue color.