I was there this past summer. Stayed on both sides. Stayed in Glacier Campground on the West side and Two Medicine Campground on the East side.
The west side of the park is more tourist oriented, which isn't necessarily a bad thing because there's plenty of stuff to do and I really enjoyed it.
HOWEVER, Two Medicine on the East side was the bomb. There is less stuff to do for sure, but Browning is just a few miles away and you can easily get all the provisions you need. There is a small store inside the park that carries probably most anything you would really need.
I got lucky and scored a site across from the lake so the daytime breeze kept us cool and the evenings got down into the 50's. Some of the best hiking trails originate from that park (so I'm told) and I really can't argue that point.
Both sides have their pro's & con's and if you can swing it, try staying on both sides. I personally felt that the East side is more relaxing because there is less to do except be close to nature.