I have 308 and 7mm08 deer rifles. The 7mm08 has no advantage over the 308win. This is my opinion so forgive me...
Recoil is the same.
Ballistics are the same.

I don't have a hunting rifle in 6.5CM so I can't compare it to the others. But speculating the recoil is a bit less over the other 2 and ballistics beyond 400 yards are better.

For big game hunting the 308win is more versatile than the 6.5cm. At the cost of more recoil.

If you want to hunt deer beyond 400 yards then the 6.5cm would be the best option out of these 3 cartridges.