I chose the Shangri-la for the chain's reputation & my previous experiences with them, and I got most of what I was expecting. Comfortable & spacious room with a view of Potala Palace, nice amenities, nice service, very good fitness facilities and a great massage at the spa.
English is not understood nor spoken by all the staff, so it can take time to get what you want, but it's not a major problem.
Fitness facilities & spa were great and the "oxygen room", which is specifically designed to help adjust to the altitude of Lhasa, was a nice extra. Major sights are within walking distance. Gift shop has nice items but exponentially more expensive than similar things in the market.
Overall, we had a great stay and would definitely return to the Shangri-la whenever possible.