I see there are still replies and readers on this question so thought it relevant to still add some more information here based on my experience from a few safaris the last 2 years. Choosing the best country really depends on what type of trip you want. If easy access, cheaper options and a more developed feel I would pick South Africa or even Kenya to some degree, however are you looking for a more rural or authentic experience, then Tanzania is a better choice I believe. When i was researching I found a few valuable articles comparing Kenya and Tanzania as a safari destination and another comparing Tanzania to South Africa as a Safari Destination. Tribes was also mentioned and while that is definitely possible in all of those 3 destinations, a real authentic experience of the local tribes in Africa you should go to Ehtiopia, Omo Valley in South Ethiopia to be specific, this isnt for safari though but might be a good destination to combine with your safari trip.
Hope whoever reads this got some value out of those articles.