We spent two weeks driving around Oman 5 years ago, and stayed (among other places) at the Chedi, Shangri-La, and Desert Nights Camp.
Shangri-La is indeed a large complex with 3 different hotels, some of them quite family oriented. We preferred it to the Chedi, though. We stayed at Al Husn, the most upscale of the three hotels. At the time, it didn't admit children under 16. It has a private beach, not open to the guests of the other hotels. Excellent service throughout. Excellent complimentary tea time every afternoon. Wide choice of restaurants, including excellent fish/seafood.
The Chedi is more centrally located (better to explore Muscat), but the surrounding area is not that great. The beach is also not that great, itīs basically in the city. Our stay was not bad - we did enjoy the design, also great food, but the service was a bit lacking. Too few sunbeds around the pool, for example, and they didn't care.
Would also recommend Desert Nights Camp for one night. Not luxury, but a nice experience for one night in the desert, and the tents are quite comfortable. We drove there by ourselves in a 4x4, easily doable.