I’ve done a bit a hunting with a 35 Whelen. Other than my hunting buddy telling me that he knows it’s me when I shoot because of the thump the bullet makes on contact, it’s not any different than a 30-06. Considering the .30 bullet technology, I would be surprised if the 06 wasn’t actually a better performer.
For hunting .30-06
For fun I’d pick .35 Whelen over the .338/06 since the 35 has a SAAMI standard, while the 338 is a wildcat and I wouldn’t assume that the 338 A-square is up to code.