Try to go very early in the day on GTS road. That way you will have more room at pull offs. There are plenty of sizable pulloffs but they are often very full. We drove it in a extended cab 8' bed Silverado with no problem. Do allow most of the day for the drive because you want to be able to pull off and look around a lot.
Parking is very crowded at Logan Pass, so the earlier the better.
If you take the shuttle, you can hop on and off at any stop. No need to look for parking at Logan Pass or other trailheads.
There is not a big elevation change on GTS Road, the biggest issue is the narrow road and overhangs and tight curves in spots.
Beartooth Pass is totally different from GTS Road. BTP is winding with large elevation changes. The pass is about 4000 feet higher than Logan Pass. There are several good pullouts and stops on BTP but not really extensive hiking trails like those on GTS road.
Trailers are not allowed on GTS Road and it would be foolish to take a trailer over BTP. Not only foolish, but very very unpleasant. Drop your trailer somewhere so you can enjoy the ride.
