The difference in recoil between a 340 & a 300 is considerable. I used to own a Browning A-Bolt in 300 Win Mag. My cousin and hunting partner owned a Ruger Model 77 Mark II in 338 Win. Mag. I fired 180 gr. reloads and he use 230 gr. Fail-Safe factory loads. I couldn't tell much difference in the recoil of each rifle. The Browning was about 1 pound lighter so this would have some to do with it. My deceased uncle once owned a Mark V 340 Mag. Firing factory ammo as he didn't reload this rifle was beyond my recoil threshold. His rifle with scope weighed about 12 lbs. with sling and ammo. This is a heavy rifle and still kicked like a mule. I would opt for the 338 Win. Mag. firing the 230 gr. Fail Safe if it gives acceptable accuracy and I think you will have plenty of gun. If the Fail-Safe load is inaccurate there are many good loads out there in weight running from 210-250 that are acceptable for use on the biggest bears.