Apgar Village has a post office and (according to others) an ATM machine.
West Glacier has the History Society's bookstore at the Amtrak Station.
I do not remember a laundromat at either place.
In terms of basic amenities, I think they are otherwise similar (both have a gas station, both have a sit-down diner, both have some local folks working at the stores who can tell you interesting things about the area).
Apgar Village has a bunch of junk touristy places (also an Alberta info center) and one good souvenir shop, Montana House, which also has hot coffee, cookies, cards, books, etc. At Eddie's, another shop (NPS Glacier has a webcam trained on it), you can get ice cream cones, bear spray, fudge, and a variety of t-shirts.
At St. Mary CG, the A loop, mostly for tents, is wooded; the B loop, less so; the C loop is mostly open and is intended for big rigs and group camping. There are showers in St Mary CG. There are good mountain views at St Mary CG, The host site is located roughly at the V intersection of A and B loops. There is a tree (or two) close in front, as I recall, but the RV site itself is not, or mostly not, shaded. For views, I would take St. Mary. For easy access to real shopping once a week, I would take Apgar CG.
Apgar CG is the first one visitors encounter driving in from the west, and often strikes me as dense with ppl and generator noise.
Montana House (Apgar Village) has a free speakers series, usually on local topics:
http://www.montanahouse.info/