We stayed 4 nights at Johnson's of St Mary's on the east side. Don't know what you are looking for as far as amenities but we loved the location and view. We also spent a week inside the park at St Mary's which we really enjoyed but no hook-ups there. We didn't stay at the Town Site campground in Alberta but did drive through when we went up to hike in Waterton. It looked very nice and the location would be great to plan day hikes from there.
By the way, you didn't ask but we prefer the east side because it has more open spectacular mountain views while the west side has more trees and more traffic.