But I meant, that if the HE isn't needed, you will have the advantage of normal .308 loads which is less recoil, agreed?
If you hand load, you can load a .30-06 down to .308 levels quit easily. On the other hand, you can't hand load a .308 up above the levels you can get a .30-06, because the case simply isn't big enough.
Come to think of it, you don't really need to be able to hand load to get those benefits. Many companies are offering .30-06 reduced recoil loads that are downloaded to .308 levels, and several companies offer light magnum loadings for the .30-06 as well.
To put it simply, the .30-06 is a more versatile cartridge.
That being said, I wouldn't feel under gunned hunting with a .308. My father took moose in Alaska with a .308 without any issues.
Also forgot to add:
a very accurate cartridge generally having a slight advantage over the 30-06 but there are always exceptions,
This is false. The .308 cartridge is not inherently more accurate than the .30-06. It may in fact be the other way around, because the '06 can better handle larger, heavier bullets which have a better ballistic coefficient.
From what I understand, this myth arose in the '50s and 60s when the .308 became extremely popular. As a result, all of the new rifle designs that incorporated better accuracy were made for the .308 much more often than the '06. Because of this, some believe that the '06, the previous ruler of the long range roost, was not as accurate. In fact, if you have two identical rifles with identical construction, but one is chambered in the '06 and one is chambered in the .308, the accuracy difference wont be enough to calculate. The '06 will probably be able to shoot flatter, however, because it has a bit of a power advantage.