Since there don't seem to be any real visible difference between an alolan growlithe/arcanine and say, a johto one, would there be any behavioral adaptations?
Mainland Arcanine/Growlithe are more likely to form packs. Alolan variants do not seem particularly concerned with each other.
This is generally believed to be due to the limited space on the islands. There simply is not enough room to support large groups of Pokémon. On a similar note, Alola’s fire dogs seem less territorial, presumably because their neighborhoods are just too small to support a land-greedy Pokémon. Some people claim this makes the Pokémon poorer guards than mainland ones, but most trainers report no difference.