If the OP is unable to shoot the better 100-105 gr 243 bullets the 25-06 MIGHT be a better option. But even with lighter 85-90 gr 243 bullets any advantage the 25-06 has is minimal.
Yeah. Only 300-400 FPS......
You can load 105 gr 243 6mm bullets to the same velocity, 3100-3200 fps, with BC's of .545. At any range beyond 200 yards the 243 has the edge in both energy and trajectory.
What .243 load sees 3,100-3,200 FPS with a 105? I never even saw 3,200 out of my 6mm, which has a decent edge on the .243 in case capacity. Highest I can find in load data and chronographed handloads is right about 3,000. Maybe you can squeeze a little more out of it, but by the same token, the .25-06 can be hot rodded, too. My favorite load is a 117 gr. Sierra with IMR 4831 that runs an average of 3,220 FPS. My hottest load is a 100 gr. TSX, also using IMR 4831, that exits with an average of 3,585 FPS.
There may not currently be bullets with quite as high a BC in .257 as .244, but some approach .5. Even assuming you can hit 3,100 with a 105 in a .243, the 115 gr. Berger (G1 B.C. .483) @ 3,200 will have a flatter trajectory to 850 yards. Even the lower B.C. Sierra Gameking will be flatter to 500. And again, that's assuming you can eek 3,100 out of a .243 shooting the heavies. I can't find any such data.
Even with a much lower B.C. of .357, my hot 100 gr. TSX load holds flatter than a 3,100 FPS .244" 105 gr. Berger VLD all the way to 950 yards.
Granted, the differences in trajectory between the two is pretty academic, since both will have the same MPBR with a practical zero range. But wrong is wrong nonetheless.