Mechanics. Pf2e is inherently tactical, and I like looking at a funky archetype or class feature and building around it. Backstory usually comes naturally when choosing what feats to take, and aesthetics usually result from that.
I'm curious to see how this correlates to the play style of people though. I come from the other side of the GM screen, and I think that's influenced how I build my characters.
I allow Treat Wounds and Battle Med to proc separately on Eidolon and Summoner. But I can see arguments for and against it.
The only thing I'll add to this discussion is to consider that the Summoner is playing two half characters. They essentially get misfortune against all AoE effects, and any buffs to their defence have to be applied twice (once to each of them). The summoner themselves is also a cloth armoured caster with significantly less spell slots than the others, making them an easy target.