Edward--I can only speak to Botswana, haven't been to Tanzania. Regarding natural beauty, wow, I can't imagine that anything would beat Botswana, as the open plains around Savuti, the waters at Little Vumbura and the oasis of Mombo that we stayed at, were fabulous!
Regarding access to medical care, Botswana is the BUSH. There are no TV's, no internet, no phones, no regular radio, just a radio communicator to the camp. And trust us, sometimes that doesn't work. The bush is not a place to get sick, and not a place to expect medical care anytime soon. If you're worried about medical care, buy emergency medical evacuation insurance, which you really should anyway. Buy insurance that flies you HOME, not just to the nearest "appropriate" medical facility. Appropriate in their eyes might be somewhat flexible, much more flexible than Americans would want....
Regarding animal viewing, to some extent, this is determined by WHEN you are going. There are several books that outline when is the best time of year for animal viewing in the various countries, and also which animals you can expect to see. Suggest that you pick up some of those books. However, it seemed to us, based on our research, that Botswana provided the best year round experience, as far as game viewing. Be advised, however, that Botswana is NOT cheap, and probably the most expensive African country, in fact. However, Botswana is committed to high quality, low volumn tourism, and thus you won't have the situation that you would in some African countries, of 10 jeeps surrounding a lion pride.. Wilderness has a rule that there will be no more than 3 jeeps at any one site, which is important..
