Taking a trip to South Africa - looking for a camera to "shoot" the wildlife

I would take the Nikon D5100, because of it's good low light performance and amazing image quality. buy it with a tamron 18-270 or something like that or a nikon 55-300 then you have a bit zoom range.

The T3i can reach farther than the D5100 (because it has a 1.6x crop sensor versus a 1.5x crop sensor).  Go with the less expensive T3i and buy a zoom lens (such as a 75-300mm) or rent the (100-400mm f/4L)