Some would consider 200 or 300 fps a significant difference.
Of the cartridges you mention, the 308 Winchester probably has the best inherent accuracy but the others can be very accurate as well. The 308 Winchester is the most efficient of the bunch.
The 30/06 doesn't really have a significant velocity advantage over the 308 Winchester in my mind until you start shooting bullets of 180 grains or greater in weight. Even then, the difference isn't that much.
For long range work, which you say you're interested in, the 300 Winchester Magnum does have an advantage. The extra velocity does make a difference. What I don't like about the 300 Win. Mag. cartridge is that, in my opinion, the neck is a little short. I know, however, that a lot of people love it.
In my opinion, the 300 Weatherby Magnum is the king of the 300 mags. If you compare the velocities obtained, the 300 RUM, 30-378 Weatherby and 300 Dakota don't do much better and use substantially more powder.
For some reason, the 300 WSM does absolutely nothing for me. The fatter cartridge means less room in the magazine and I don't think it's any better than some of the .308 caliber cartridges already available.