On the positive, the 338/408 is going to be much faster on velocity. You pay for that in the shape of the trajectory, and at ranges past the maximum ordinate range, or 60% of the total range, your fall angle is going to be steeper. This is a "danger space" dimension that gets shorter as your fall angle is steeper. What this all boils down to is, YOU HAVE TO BE MUCH MORE ACCURATE on your range to target. As that target gets smaller, the MORE accurate the range has to be.
The gun with a velocity in the 3000 fps range will have a long range advantage in this case. Velocity does not gain you much supersonic range, it only gains you a "cheat" in the trajectory BEFORE maximum ordinate. That's where guys are referring to when they say "it shoots flatter". It only shoots flatter in the "rising branch" of the trajectory. If that's where you plan to shoot, then you are fine. With rifle of 2200 yards of supersonic range, that "rising branch" is about 1400 yards. Then it becomes falling branch, which is where the danger space dimension is critical. This is kind of a spinoff discussion from before about guns with very high velocities having their projectiles slow down faster. That points was missed in that guys focused on a projectile actually "passing" another that is launched slower, it doesn't work that way.
3000 fps has an advantage in that it doesn't burn out barrels. A .768 BC bullet is only supersonic to "x" yards, changing he velocity only changes that supersonic range from 2900 fps to 3400 fps gives you a supersonic range gain of 21% (NOT using a standard G1 ballistic co-efficient, but real data). That's a good gain, BUT, the danger space dimension is much shorter at 2300 yards and 3400 fps, than it is at 2300 yards and a muzzle launch speed of 2900 fps.
It gets much deeper than this though. Add in the additional cost of powder, brass, and barrel wear, the high velocity guns are $$$ demanding.
Just my ,.02