The 308 is one of the best cartridges ever. The 7mm08 is also great. I have shot both alot and I think the 7mm08 has some advantages. Better BC for the same velocity, you can use same cheap brass and if you use 308 brass for making 7mm08 cases you have a thick neck that can be turned to fit chamber of any rifle.
I used 162 grain Hornaday match bullets in my 7mm08 with a case full of H414. Didn't have a chrono at time so don't know how fast it was going. This load shot great.
I have just gotten hooked on this long range shooting and am still learning. Bought a Winchester Coyote in 7mm WSM to try. I think this cartridge has alot to offer. A 168 grain at 2900 fps shoots great and is very flat shooting. Bullets for the 7mm are getting better and more weights are available. Its not quite as good as the 6.5 in BC or in number of bullets to try.
One big advantage to the 7mm08 or 7mmWSM is you can buy a good rifle off the shelf without having to build one.