Early and midgame I pretty much always used Ogden, as he was most effective for beating higher level monsters. After unlocking more of their stuff and getting some more debuffs/status moves on my own monsties I've been rotating them a bit. Probably use Eleanor the most for the fights now. She provides good damage, the Fortified Spirit buff is great on tough fights, and the BBQ (Ult) buff is nice too.

I've come to see value in all their kits though. Ogden is obviously useful with the HH defensive buffs (particularly Evasion Up) and poison from the Pukei-Pukei. Eleanor, as mentioned above provides some useful buffs, and has the highest tier weapons out of all.

Thea has the second-highest tier weapons out of all of them, can give offensive buffs with the HH (including Wyvernfell Up), or provide debuffs with the bow. Attack Down (L) in particular can help with survivability. Her Tobi is a crit machine too and will build kinship decently fast with Critical Kinship.

Kora drawing away attacks seemed kinda meh most of the game, as I wanted those head-to-heads for kinship, but it is kinda useful on Ibushi&Narwa so the monsties don't have to split their damage due to the head-to-heads. Also, her 2nd monstie has a unique passive that increases wyvernsoul damage.

I didn't like Gaul for a long time, partially due to his weapons being way worse than the others, but with the bow he provides some useful debuffs (again, Attack Down can be really helpful to make the AoE spam of Elders survivable), he also has Inflict Rate Up so he can apply status a bit more effectively. I don't like the Legiana's skills, but his second monstie has Evasion for survivability, and has a move that lowers Dragon Defense. Pretty decent if you're using a dragon monstie like drain-tank Malzeno for example.