We're a Tanzanian operator, so this is unavoidably biased — but we'll be as honest as we can.
What Tanzania does better
• Sheer scale — the Serengeti is twice the size of the Maasai Mara
• Ngorongoro Crater (Kenya has nothing like it)
• Lower vehicle density in most parks
• Zanzibar for the beach add-on
• Kilimanjaro for the climb add-on
What Kenya does better
• Cheaper international flights from most origins
• More direct flights
• Tighter Mara crossings (more concentrated)
• Easier short trips (3-4 days)
The migration question
The migration is in Kenya's Maasai Mara from August to October, and in Tanzania's Serengeti the other nine months. If you're chasing one specific window of crossings, Kenya is often easier. For everything else, Tanzania is the better choice.
What we'd recommend
First-time African safari? Tanzania. Repeat safari-goer looking for variety? Kenya next. Have time for both? Combine them — Serengeti + Mara is one of the great trips on earth.