RAT does not as of yet make a knife that is a good chopper, so let's just throw that condition out the window for right now. EDIT: They do now, the mighty Junglas which will be available soon! As batonning, the RC-5 is fine. So is the RC-6. Both are going to work pretty similar. You whack them with a baton and they go through the wood. Nothing to base a decision on. Now when we get to the finer work such as carving and trap making, you can go ahead and take the RC-5 right out of the running. That 1/4 thick blade with a relatively fatass grind isn't going to work nearly as well as a thin full flat grind for carving or slicing. That grind, the whole knife for that matter, is designed to be a tough barbarian sword of a knife, useful for cutting apart helicoptors, tanks, enemy forts, etc. It's not meant to be a woods knife. The RC-6 is designed to be a good all around middleweight/large camp knife.
Now here is the other option. Mind you, if you're wanting one of the bigger ones simply because you're into bigger knives, more power to ya. However, if you looking for the best knife to fill the needs you described, aside from chopping of course, than these are too large. The RC-4, whilst being slightly larger than the standard "polite society" EDC knife is really ideal. It is very similar to the RC-3, just slightly beefier and more suited for batonning and such. It would make a fine camp knife and also be easily concealable (at least much more so than a 5 or 6) for EDC.
Then you ask, "well then what am I going to use for chopping?" The truth is, no knife is as good for chopping as a decent machete, hatchet or axe. Find a cheapo of one of those three choices, probably better off with the machete as the Asheville mountains have a good bit of viney stuff if I remember correctly, and pair that with the 4. Another EDIT: RC is about to release the "Lite Machete". I know that this means adding another piece of gear, but believe me, and everyone else who will agree with me, it is more than worth the extra weight when it saves your energy. What you can chop with a camp knife, you can chop 10 times faster with a machete. Having a do-all knife sounds cool. Having a great knife AND a proper chopper is pracitcal and smart.