Over the last several years I've had a resurgent interest in hunting with lever rifles and also big bore lever rifles. I have lever guns in .356, .358 (actually medium bores), .375 Win, .444, 45-70 and 450 Marlin. I also have a couple in .308, one a ME and the other a .308 Win and also have one in .325 WSM. The medium and big bore levers are not really as punishing as some think, when using moderate loads. If you were to compare a typical 180gr 30/06 load with a 405gr 45-70 load (factory 1330 FPS) you would find that in like weight rifles, the 30/06 has slightly more recoil than the 405gr 45-70.
The 300gr 45-70 load at 1880 FPS is slightly heavier recoiling than the '06/180 and 405gr. These loads will kill game at ranges that might be difficult to take advantage of, due to their rainbow trajectories. They will both work well to about 125 yd MPBR. A step up in power, recoil and trajectory is found with the LeverEvolution ammo, giving the hunter a MPBR of about 185 yds or so. There are heavier still loads in 300, 350 & 400gr bullets that will cleanly take anything in N.A., but these are pretty heavy recoilers.
The .444 will recoil slightly more than the lower factory loaded 45-70s due to much higher velocities in it's 240 & 265gr loads. The added velocities do tend to make it a better choice trajectory-wise though with a full 200 yd MPBR found with these loads. The .450 shows heavy recoil with either of it's Hornady factory loadings, being almost exactly the same as a similar weight .338 WM shooting 200-225gr loads. I find the .375 Win and .358 pretty easy on the shoulder, but any Marlin or Winchester lever gun in .375 (or .356) or BLR in .358 will run a good bit more $$ typically than a typical .444 or 45-70. If you were to find one, the .375 is a very fine woods rifle, however. And the BLR in .358 is a great rifle with a lot of versatility, making it way more than a short-medium range woods rifle.
My favorites at the moment are my two Guide Gun sized Marlins (18.5" barrels), one in 45-70 and one in .450. They are very handy to carry and hunt with. I actually sold my 22" 1895 to replace it with a Guide Gun. They did also make the .444 with a shorter barrel for a time (.444P), but they are all also ported and not all hunters are fond of ported barrels.