I have a model Seven Remington with a 21" Hart barrel chambered for 358 Win. I love the rifle, I have killed a coyote and one whitetail with it. I load my own ammo, 200 grain Barnes TSX, but once I use up what I have I am going to try the new Buffalo Bore 225 grain TSX @ 2500 fps. I can't even come close to that with my handloads, so as long as they are accurate, I'll stick with them. The 358 can be loaded with 180 grain bullets at around 2800 fps, which is pretty much identical to the 30-06(barring BC).
The buck I killed was 189 lbs dressed, and at 197 yards I punched through him twice with the 200 grain TSX, so I would say the 358 has plenty of power still at that range. 3" high at 100, dead on at 200 and 10" low at 300. It works out in my scope so I can hold on the point where the reticle changes from wide to thin above the crosshair at 100(for +3"), hold dead on at 200, and then just a hair below the reticle changeover below the crosshair at 300. I use the Bulletflight program for farther than 300 but I doubt I'd actually shoot at an animal past the 300 yard mark.