Tejano & Brooksrange: I actually have owned, shot, used and Hunted with both cartridges for many years now - my opinion - it's a tie!
Both are outstanding cartridges on out to 500 yards or a tad further.
Many years ago I had the world class riflesmith (and rifleman - he won the Wimbledon Cup back a ways!) Jim Cloward build me a heavy, long (27"!) barreled custom 240 Weatherby on a pre-64 Winchester Model 70 action.
It has been a dream Rifle since day one!
I remember my friends "cautioning" me about the inability of the 240 Weatherby to attain "good accuracy" do to the "rounded shoulder" of the 240 Weatherby cartridge!
My friends were wrong - REALLY wrong.
My Hart barreled 240 Weatherby is extremely accurate - every bit as accurate as my custom 6m/m Remington Ackley Improved or my Remington 40-X's in 243 Winchester and 6m/m Remington.
I have several Varmint weight Rifles in 25/06 Remington and one 25/06 Remington sporter weight Rifle - wonderfully is how I would describe their performance.
Wish I could "settle" your conflict about the 240 Weatherby vs.the 25/06 Remington - declaring one to be better than the other would be the riflery equivalent of blasphemy, IMO.
My 240 Weatherby brass has good case life and I have not been in a bind to find enough to support my needs.
Hold into the wind
VarmintGuy