In my opinion the 358 is the way to go. I have used it on elk and with 250 gr. Hornady bullets it's close to the perfect timber cartridge. I've used the 225 sierras also on elk , kills 'em dead. The real advantage of the 358 vrs. the 338 fed is that with the heavy bullets( 250gr) the hornady bullet is much shorter and allows for more powder in the case. A 338 250gr is a long bullet and restricts power capacity. I shoot 2550 with the hornady bullet out of my steel receiver BLR. The 338 fed may shoot somewhat flatter but the 225 gr sierra has the BC and will almost match the longer bullets
They will both get the job done well---personal choice
You'll never even remember the recoil in the field, they are not bench cartridges and were never intended to be.
Good Luck and Good Hunting
Lj