I think both are great rounds shooting nice & flat trajectories with similar accuracy. The main differences are bullet weight and case capacity.
The .243 goes from 60 to 105 grains and the 25-06 starts at 75 grains and goes up to about 120 grains. So if you are going to shoot only small deer & foxes, the .243 is fine and if you will mostly shoot skia or reds you would be better served by the 25-06.
The .243 case is short and only needs about 60% as much powder as the 25-06 so it is cheaper to reload.
Also being shorter the .243 rifle will usually have a shorter action and be quicke
