RM has a reputation for fine lodging and service, but many of the safari purists are put off by the visibility of a fence on or near the property. Some say it makes the place feel more like a zoo. Singita will have equally good accomodations and service but will feel more natural and wild. Plus the game viewing (and guiding) is always rated tops for numbers and variety.
For the very best info on both, go to fodors.com. Click on Talk and drill down into the Africa forum. You can search for info on both and read loads of detailed trip reports.
If you have the time, you should also consider Botswana for the ultimate "Out of Africa" experience. The luxury tented camps are amazing.