Only difference weight wise between a TC Hawken (no "s") and a TC Renegade is about half a pound. Difference in barrel length (same caliber/charge - velocity) is not enough to worry about at the ranges they would be shot deer hunting. The lighter weight, shorter barrel, lack of brass flash and stock design do given the Renegade some small advantages over the Hawken hunting, especially spot and stock. If you can find one, the Renegade also came in a single trigger "hunter" model that is easier to use with gloves on in cold climates than the double trigger model or the Hawken that only came with DT's.
For just deer either a 45 or 50 is enough even for big deer, you don't need a bigger caliber even out to 100-125. The bigger cals will make up for poor shot placement though, something to consider maybe as you are new at these - may not yet realize that they are not going to shoot the tiny groups cartridge firearms can, not even at much shorter ranges. Ethics must come into play with traditional smokepoles even more that cartridge firearms... not take questionable shots beyond what you are confident you can do - every time. With some folks, 50 yards is their max range for deer hunting with their muzzy, well beyond 100 for others, and with the serious target shooters..... well. What your effective hunting range will be in the beginning will be less than what it will be later with lots of practice. Getting use to their slow lock time and ignition, just lobbing lead, etc have to be learned.
Some folks discount round balls for hunting and prefer the heavier maxi balls or cast bullets. Over kill IMO, a RB does an excellent job on big game much larger than deer. I hunted big western mule deer for years with 50's, elk and bear with 54's, deer again later with 45's, and always with round balls. I also always used real and not plastic powder, and never felt the need to shoot max loads. As is typical in the west, ranges could be longish even though I was always a spot and stock hunter (stands wasn't hunting to me). And I often had to deal with wind strong enough some times that I had to give a free pass rather than chance a bad shot.