RE: How to handle recoil
T/C.
Assuming you are true to your name sake, and you are talking 300WinMag versus 308 barrels on a T/C frame then I bet the 308 certainly is more fun to shoot than the 300WinMag, as the whole rifle isn't beefed up from top to bottom (heavier) to accomodate the stronger mission thus leading to a drastic jump in recoil. 308 is absolutely one of my favorite paper punching cartridges, a real joy for sharpening up at the range.
Those who are uncomfortable (regardless of reason) with the recoil of rifles chambered in larger cartridges are definitely better served by something less robust. As the vast majority of the readership tend "max out" at hunting deer then this shrinking back in cartridge strength works reasonably well as deer can be knocked over with a stick.
Moving up to larger game, got to be careful with the old and weary "dead is dead" mantra, otherwise we could all be argued down into shooting 22 Hornets. The key distinction is "dead where." Dead in your possession or out there in the field somewhere? That is where one of the greatest fallicies of Internet Forums comes to play. Someone succeeds in taking down a grand game animal with a marginal round and it's automatically posted as the gold standard of how to do it. Let the same hunter attempt the same thing and the critter gets away and suddenly it is his "dirty little secret" never to be told in either the bar or on the 'net. Both critters are dead; however, there is a significant difference between the two -- one is in the hunter's possession, the other is coyote fodder. Again, not talking deer sized game here.
EKM