Hi and welcome to the site.
As you know the Teryx is a lot taller and a little wider than the RZR, so if your trails are made for ATV's then you may have to do some cleaning up in order for the Teryx to fit in all of the trails. I was looking at the RZR as well before I decided on the Teryx. I chose the Teryx because I hunt often and liked the utility of the Teryx. The RZR is all sport where the Teryx I feel is ultility first and then sport. The RZR seats were a little too low and the bed space was not big enough. I prefer to slide in and out instead of fall in and climb out. While test driving, the RZR was a little faster, but I liked the suspension on the Teryx a lot better.
With the addition of a CDI box and exhaust tip, I out ran a stock RZR in the river bed the other day. The guy told me that he had more pedal, but could not keep up due to the bumps. The Teryx loves rough terrain, the faster the better. We took it to hard pack, and the two machines were neck and neck. I'm not sure about the stability of the RZR, but the Teryx is a very stable machine. I have gone up and down 80deg inclines without a problem, and have taken turns way to fast without a hint of the machine wanting to roll over.
I'm not sure how the RZR performs in the mud, but the Teryx is bad a**. I put a 4000 lbs. winch on my Teryx and have never needed to use it. This machine will go through just about anything.
The best thing to do is just drive both machines if you can. And make your decision from there. It took me 4 months to make up my mind, and I don't have any regrets for choosing the Teryx.
Hope this helps,