The Savage Alpine Trail on the west side of the mountain is known for being steeper, rockier, and having more switchbacks. That being said, this part of the trail is also a bit shorter than the north side. Some people choose to come up this steeper way and run down the north side, but you can run basically every step if you decide to do it in the opposite direction.
There are some steps cut into the trail on a couple of occasions on this side of the mountain that you'll need to be careful on, but there are always views you can stop and admire.