308 doesn't recoil at all.
While the recoil of a 308 is by no means bad it is definately more than 7mm-08.
if the .308 kicks a little more than the 7mm-08 there are things you can do to make it kick like a 7mm-08.
Yeah but those same things that will make a 308 kick like a 7mm-08 will make a 7mm-08 kick like a 243. Hands down a woman or child is better off with a 7mm-08.
And while thereare more types of 308 ammo out there there is by no means a limited selection of 7mm-08. 14 different options at the one website where I checked in fact. If one of those 14 don't fit your needs then it's time to start reloading.