The annual migration is an irregular clockwise movement of approximately 1.5 million wildebeest, gazelle and zebra around the larger Serengeti eco-system.
To catch the action you need to look at Tanzania’s Serengeti or Kenya’s Masai Mara at any time of year except April and May when the “long” and deep rains have set in.
Main access is via Nairobi (Kenya), Arusha or Dar es Salaam (Tanzania) and to keep costs in check you ought to concentrate on one or the other….
Tanzania’s northern circuit (Serengeti, Ngorongoro, Tarangire, and Manyara) is best for the migration from January to April in the southern Serengeti. Again from August to November in the north. Beyond the migration you’ll find outstanding wildlife with resident big game in the south and west of the country (Selous, Ruaha, Katavi, and Mahale). Some good beach options on Zanzibar and Pemba. If you’re after wildlife, volume and variety then Tanzania is a better choice than Kenya.
Kenya‘s Masai Mara is at its best for the migration from July to October. Ideally combined with other more diverse habitats (Amboseli, Laikipia, Meru, the Northern Frontier District and the Rift Valley). Then the beach spots around Lamu and Malindi. If wildlife is an interest and you’re also interested in culture and a beach break then Kenya’s a better bet than Tanzania.
https://www.zambezi.com/blog/2015/planning-next-african-safari/