Beatrix is an interesting mixture of those two. Her personality is certainly more Dragoon, but at the same time, she is heavily military-minded, since she's the General of all of Alexandria's forces. It could be argued that she's that way because of her devotion to her queen and country, which then switches to devotion to Garnet in the latter half of the game.

I really don't know what to do with the Paladins, honestly. Cecil is a good fit for Soldier because his Dark Knight/Paladin sides cancel each other out, I think, but Agrias and Beatrix are a LOT more hazy.

Basch I would put with Dragoons, I think, because he has the personality and the devotion to one person/cause (Ashe, then Larsa).