You may not know it yet but Tanzania is one the best destinations to observe wild animals. Usually, people think about Kenya and its Serengeti Park (which inspired the scenery of the Lion King) but most of the second biggest African Safari Park (National Kruger Park, South Africa, being the biggest one) is actually located in Tanzania.
Is it reason enough to chose Serengeti? Maybe not. The country has several national parks which are less famous and it can be a real advantage. A lot of tourists go to the parks of the North (Serengeti, Arusha, Ngorongoro, Kilimanjaro) and you often have to queue behind a few cars before getting really close to the animals. So if you’re looking for peacefulness and a really wild experience, you might as well go to the parks of the South. I personnally went to Selous Game Reserve which has the advantage of being closer to Dar Es Salaam (the economic capital). We felt alone in the world and can only regret not seeing rinos.
To sum up, parks of the North probably offer a wider wildlife but if you want to experience a real wild adventure, parks of the South are also a good option.