The .25-06 will have a bit more felt recoil, and use up a lot more powder too. The .243 87 VMax is simply the best bullet out there in either .25 or .243 in my opinion (don't know the .25's that well, so I could be wrong). I think Hornady makes a .25 VMax at 87, and the .25-06 will launch it faster than the .243, but its BC might be a tad lower, not sure.
For cheaper shooting and less recoil (= more rounds downrange), the .243/6mm is hard to beat. What is said above regarding luck and skill is correct. Past about 400 shots get very iffy as to elevation and windage. You really need a buddy to spot your impacts for you when shooting way out there. A quality scope with excellent adjustment mechanism is a must as well, we're talking top drawer stuff here, not Tasco or Simmons etc. Weaver target scopes, Leupold with target turrets, etc. And learn how to read the wind mirage.