I used 30-06 almost exclusively for 40+ years until about 7-8 years ago when I made the switch to 308. If I were going to Alaska or Africa I'd choose my 30-06 10 times out of 10 over ANY other cartridge short of 375 mag. I've seen too much data and too many successful hunters, prove that rounds like 45-70, 35 Whelen, 338-06, even 338 WM offer no advantages over 30-06 loaded with 200+ gr bullets, in fact all most of them do is recoil a lot harder than 30-06. The various 300 magnums do exactly the same as 30-06, just farther down range and with more recoil. There just isn't nearly as much data and real world experiences to prove it, but I strongly suspect a 308 loaded with the same 200 gr bullets would be quite effective on the larger game in Alaska or Africa, of course at reduced ranges. But most people just never think of loading bullets that heavy in 308.
Why do I now prefer 308?
In the same weight rifles I get about 20% less recoil. Or I can put together a rifle that weighs under 6 lbs scoped with recoil exactly the same as my 7.5 lb. 30-06. That recoil reduction may not seem like much, but when I go to the range I simply find myself shooting the 308 a lot more because it hurts less at the end of the day. More shooting equals more confidence in the rifle. I find the 308 a bit easier to get better accuracy from too, probably because I shoot it more.
Todays 308 loads beat 1950's era 30-06 loads by about 100 fps. It was the post WW-2 era that cemented the 30-06's legend. I don't see how a round shooting the same bullets 100 fps faster is a negative. Of course modern 30-06 loads are even better, but can I take advantage of them? My 308 loads give me almost exactly the same energy and bullet speed at 400 yards that I'd get from 30-06 at 475 yards.
I'm also a realist! At one time I dreamed of hunting in exotic places for really large game, but I know that will never happen. My 308 serves me well, and if I ever win the lottery and can afford Alaska or Africa I'll go a lot bigger than 30-06. I live in GA, a sub 100 lb deer isn't unusual and the biggest animal I'll hunt here is black bear. Around 200 lbs is about average, but we've had several well over 500 lb taken and a few over 600. Realistically an elk is the largest game animal I'll ever hunt.
I feel perfectly confident in my 308 rifle and my loads to be able to hit and cleanly kill an elk at 400. My 30-06, shooting the same bullets gives me about 50-75 yards more effective range. Is it worth carrying a rifle 1 1/2 lbs heavier for the odd chance of a shot slightly beyond 400 yards? And can I make that shot? Right now 400 is about as far as I'm comfortable. If I were doing it over as a young man I'd go 308 for an all purpose round, skip right over 30-06 and go with one of the 300's for ranges beyond the capability of 308.