What Tanzania offers that Kenya does not
Space, mainly. On the short grass plains you can drive for an hour and see one other vehicle, which changes what a sighting feels like. The Serengeti is roughly seven times the size of the Maasai Mara and it has no fences on the Kenyan side.
Then there is the crater. There is nowhere else in Africa where a single day produces so much, and it is the most dependable place on the continent to see black rhino. Rim lodges give you cold mornings and a view straight down into the caldera before you descend.
Calving season, January to March, fills the southern plains with wildebeest calves and the predators that follow them. Tarangire adds very large elephant herds among baobabs in the dry months, and the Serengeti is the classic balloon flight.