You looking to pack through dense cover, etc? One time deal, or possibly something you do for a long time? Strictly hunting, or more for defense? All those factors could weigh in. I pack my GG in the bush for work, have packed many different rifles and shotguns for extended hikes (from 5 km to 20 km) through some easy and some real tough terrain, including steep mountains and heavy, thick regen (brush). I find long barrels and anything hanging off the thing (like a bolt handle) does nothing but snag on branches, bang on trees and generally cause a guy a headache.
I know guys who do indeed pack bolt actions and swear by them - I personally prefer the .45-70 GG because I find it carries the best of the various rifles and shotguns I have carried. I could (and really should) get an ATC but boy when you see a grizz within punching distance...something comforting about the .45-70 there. Not that I've had to shoot a bear in self defence, but I have been nose to nose with a few.
The GG is also fast handling - though a bolt is too in the right hands. I can have it ready quickly. I DID have to do a lot of action work on it after I bought it (and yeah it is pre-Remllin) to make it work reliably but it does so now. No jams, it just works. Recoil...with a real healthy load you would notice the recoil. It is substantial. Keep to factory loads and it is comfortable, Trapdoor loads are absolutely pleasant and I can run 100-200 through at the range with no problems, it's just plain fun at that level.
Durability? I have literally tossed my GG into a swamp getting out of helicopters and such, and smacked it against trees, bounced it around in trucks...I've fallen off logs and landed on it. It shows its treatment but it still works and shoots fine. Open iron only (no front sight shroud, it caught on every friggin thing in sight so I tossed it first day out) so dunno really how accurate it is, but I can hit a boiler room sized target every shot at 100. Good enough for my purposes.
At the end of the day, and speaking from experience hiking around with rifles and shotguns since the 80s anyway, this is truly something you have to try out and decide upon by trial and error IF you plan on doing a ton of this stuff.
Your first choice, be it .338 or .45-70, likely won't be your last, if you stick with it.
Whatever you decide there, good luck