Ease of getting entry visas is about the same in both countries especially for a weeks vacation.
I assume you will be staying at lodges as part of your package holiday when on safari, therefore English will be spoken wherever you choose, all lodges normally have English speaking staff.
Law and order, if by this you mean a stable country then both are pretty much the same, if you mean crime rates then Tanzania is generally safer, SA has high crime rates in some of it's cities.
Adequate medical care, is there a known problem and is that why you are asking? if not them health care is an issue wherever you go in Africa out side of cities, I assume by going on safari you intend to be in the bush. Most lodges will have an arrangement for medical cover and have first aid treatments again if there is a specific issue you should let them know in advance.
You'll need to let whatever lodge you intend to stay at know of your dietary requirements prior to going to ensure they can cater for you, bush lodges by their very nature do not have easy access to shops, this will give them time to get in things for you, food hygiene has never been a problem in my experience. I run a lodge in Northern Zambia deep in the bush, I also need to know my clients dietary requirements prior to a visit as getting supplies in can be difficult at short notice as long as we know in advance we can meet most client requirements.
For example we have catered for , vegetarian, vegan, lactose intolerant, Halal and Mediterranean diet .
Ask your travel agent to contact the lodge for you to let them know your requirements.
Personally I would opt for Tanzania, the game is better by an large and usually slightly cheaper