I haven't been to AC, but I go to Placencia every year and in fact will be there next week for the rest of June.
Placencia - boat rides are longer, so lunch will be served on a caye. Splash Dive Center is the shop of choice, but some of the hotels have their own in house dive ops. Great beaches up and down Placencia. Also, very easy access to the jungle if you're so inclined. The village isn't quite the tourist centric location that is San Pedro, but there are plenty of restaurants, bars, sandwich shacks, etc to choose from.
AC - has more of everything and is where the bulk of the tourist trade goes. Nothing wrong with that, and in fact helps keep the lines shorter in Placencia for which I am grateful.
Splitting time? I would think more like 14 days would be the bare minimum if I wanted to split time. The logistics of going from one to the other is going to take a pretty big bite out of a precious vacation day. If I were only doing ten days, I'd rather stay put, at least until near the end, then go back to the mainland and check out the stuff to do there before hopping a plane. You can always go back and stay at the other place next time. Otoh, getting there is half the adventure, and I see package deals all the time for 3 days on the beach followed by 3 days in the jungle or vice-versa. Not my preference but ymmv.
Maya vs Tropic. No difference, really. For whatever reason, I prefer Maya.