If you're worried about the unrest in Zimbabwe, I don't think you'll find Moz much better at the moment, and perhaps worse. They actually have an insurgency going, although it (currently) appears "manageable." Personally, I wouldn't worry about going to Zimbabwe. Your PH will pick you up and whisk you out of town before you have a chance to see a protest. And it will be like the "good old days" - they will love to see fresh, crisp, US dollars!
I have hunted buffalo in both RSA and Zimbabwe - multiple times in each. The hunts can be as similar as you want them to be, or completely different. In Zimbabwe, the hunts tend to be for free ranging buffalo on large concessions. Success depends on a number of factors, including the amount of rain (more is bad), and your ability to walk. You may find that an area which had large numbers of bulls last year has very few today. Equally, if there has been little rain, you will be able to get on tracks much more easily at the few(er) waterholes remaining. In both cases, that's hunting.
You can also have traditional tracking hunts in South Africa, but you will likely (but not necessarily always) be in a fenced area. It might be tens of thousands of acres, so I'd suggest it's essentially the same a free range (at least I haven't found any meaningful difference), but you have to make that determination for yourself. The biggest difference between Zim and RSA is that in South Africa, you can make things easy for yourself if you want, because you will know the buffalo are there, and you can drive around until you find them. Some PHs will want you to hunt that way - if you don't want to, you just have to make that clear.
Personally, I think it would be a shame to hunt buffalo other than in the traditional, tracking, manner. On foot. You can have that experience in South Africa. You just have to ask for it.
