Expedient - I just returned from a business trip to Cairo two weeks ago. What a place!
I can't speak much to the other 3 or 4 other Sheraton hotels, but we stayed at the Sheraton Royal Gardens.
It was a very pleasant stay. The rooms were large, the lagoon pool and whirltub were attractive, and the service polite. It's a much smaller hotel than the others (use to be a private residence/mansion and was expanded) and I liked that feel!
If you're looking for somewhere quiet, away from the hubub of Cairo (and there is A LOT of hubub) with good proximity to the Pyramids, then I would definitely go with the Royal Gardens. It's a bit of a ways from the airport though... so you get a great tour of the city just driving there!
Enjoy the trip!