I think this really depends on how long you have. Both countries are far bigger than they look and it takes time to move around.
If you only have two weeks then I’d suggest focusing on just one of them. Tanzania is a little more expensive than Kenya and perhaps less kitted out for family tourism (though it’s not a big difference).
The parks are generally beautiful and varied in Tanzania. But, saying Tanzania is quieter and especially more varied than Kenya is a common, but false, misconception.
In fact, Kenya has more scenic variety ranging from the tropical coastal beaches, the classic East African savannah, mountains, rain forests, farmland and, in the north semi desert and true desert. Tanzania has all these but not the desert.
And yes, Kenya’s Masai Mara is busy but if you go to one of the surrounding conservancies then you get the same wildlife experience but with minimal numbers of other visitors.
To summarise then I would say that Kenya is the better bet for a family holiday (I have a 15 and 12 year old and would choose Kenya over Tanzania for them).
