I know nothing about Eagle Mountain Outfitters. However, I rifle hunt 54 and set up camp in the parking lot where Tenderfoot parks their rigs and head out to their camp. I've watched this outfit pack up and hit the trail with their hunters the day before season for the last 3 years. I would think you would be hard pressed to find greater bunch of guys to book a hunt with. I've visited with them briefly while they were getting ready to go and its obvious they know what they are doing and trully enjoy outfitting.
That being said, you are wise to book an outfitter for the West Elks if you are new to the area and do not live nearby. I see lots of hunters hunting the area but very few who hunt their every year. Most hunt 1 year and then don't see them again. There is good reason for it, and good reason why there are always leftover tags for 54. There are elk there to be sure, but the area is definetely challenging.
If you book with Tenderfoot, I'm sure you won't be disappointed.