Menus aren't the same, although their offerings are similarly a mix of pedestrian fare & African fare.
Boma was "meh" for us. It was fine, but not memorable and the seating was sloooooowwwww, even with ADRs.
Tusker House was a surprise favorite for us after we ate there simply to get preferred seating for the Nemo show when that was in high demand many years ago. We eat there once every trip now.