First of all, I've been shooting .270 my whole life and don't reckon I'll ever change, so long as I'm hunting North America. I might move up to a magnum cartridge should I ever go out for moose, but that won't likely be the near future. And I've never hunted with 7mm-08. So I'm quite biased.
Anyways, although I'd personally opt for the extra oomph of the .270, which I really don't think is too much (been shooting it since I was about 10), I'd say decide what type of rifle you want for what style of hunting. Even the kids should be able to handle the .270 if they're shooting a full sized rifle (like a wood-stocked Rem 700), out of a box stand, with a good seat, and a sturdy rest. So if that's your speed, don't handicap yourself.
If you're going to be hiking all over the back country, stalking game, or hanging out of a tree shooting free-hand, and subsequently prefer a lighter rifle like a Rem model 7 or a Savage, I could see a strong argument for the lighter recoiling 7mm-08. Especially for a kiddo shooting from a less than ideal stance.
Never heard of a 270 super.