There really will be many of the same menu items at each location, although Boma may have a few more "upscale" options, for lack of a better word. Also, it will be A LOT quieter at Boma, not only because of the character draw of Tusker House, but because it is in the resort and many other people will be heading to the parks around breakfast time. We went to Boma for breakfast during out last visit, and had an amazing experience not only because it wasn't terribly crowded, but because the service was wonderful.
We've had great service at Tusker House as well, but it's a bit more frazzled. All in all though, the food is very similar, it's the atmosphere that's very different from the two!