It's kind of like debating which is better, a 302 or a 318, or a 350 or a 360. One is slightly larger than the other, and if you apply similar levels of technology to both, the larger will perform slightly better, while the smaller will be slightly more efficient.
If you're talking about "stopping power" in terms of killing something, I really don't think anyone or anything is going to notice the 200 fps or less difference between a .308 and a .30-06. They're too similar for it to really matter. There are too many other factors (shot placement being a big one) that matter much more than cartridge selection. You might appreciate the half pound or so you'll save in rifle weight, but that's about it.
If you're talking about "stopping power" in terms of killing something, I really don't think anyone or anything is going to notice the 200 fps or less difference between a .308 and a .30-06. They're too similar for it to really matter. There are too many other factors (shot placement being a big one) that matter much more than cartridge selection. You might appreciate the half pound or so you'll save in rifle weight, but that's about it.