I have a .54cal GPR and several T/C Renegades & Hawkens in .50, .54 & .58cal. The GPR is an excellent shooting rifle but needs a bit of tweaking, after taking it out of the box, to shoot the best. New, they have very sharp lands and you need to polish the bore to get best results quickly. I also am not real fond of the stock sights but by opening the notch on the rear sight and painting a yellow bead on the front blade I improved mine a great deal. Accuracy is as very good, as good as you can get in a production rifle, and better than the 1:48" twist T/C barrels. I personally like the longer barrel of the GPR better than T/C's shorter barrels.
The T/Cs are very well made and T/C's warranty is the best in the business. I prefer the Renegades as I do not like the brass on the Hawken model and have purposely tarnished the brass on mine so it looks more traditional. T/Cs with 1:48' twist barrels will shoot patched balls quite well, better than many people think, but I do think the GPR is more accurate, especially with the higher powder charges. Now my T/C Hawken, with a .50cal. GM barrel, has the length I prefer and shoots round balls exceptionally well. My favorite rifle is a T/C Renegade with a .58cal barrel. It is the most accurate shooting rifle I have and will certainly handle all the big game you mentioned. I like the .58 so well that I am getting ready to build my first rifle and it is going to be a full stocked Hawken in .58cal.