Only real difference is that the 25-06 would get you out a little farther with a heavier bullet. Doing the ballistics on it, the 25-06 would get you out to about 500 yards and safely take a deer. With the .243, using a smaller bullet, you will be able to safely take a deer at 300 to 400 yards at max. This is just my opinion while putting the numbers through hornady's ballistic calculator.
My choice would be the 25-06. Recoil is not bad at all and gives you a little further reach. So why not go with the 06? It can even double as a good varmint gun too. Ammunition is out there and can be ordered online.
Haha..or just buy him his own .270