Hands down the .243 will have less recoil. And it has plenty of power for deer. I use 100 grain Winchester Power Points in mine and they drop them. My dad has two artificial shoulders that are titanium. He had to quit using his .30-06 because it hurt him too bad. We got him two Remington Model 700SPS rifles. One in .243 and the other in 7mm-08. Neither one recoils very much but the .243 is less. I lent ours to a 9 year old to use in rifle season this year and he said it was nothing to shoot it. Already asked us to borrow it again next year.
I bought my wife a Weatherby youth compact in 7mm-08. Fits a smaller framed hunter perfectly, recoil is not noticeable and is very accurate. 7MM-08 is a perfect deer/bear gun for PA. They also make a reduced recoil load for it if your grandson is sensitive to the recoil of a normal load. IMO the 7MM-08 is hands down superior to a .243 for deer. You may also want to consider a 6.5 Creedmoor.
My grandson doesn't like to shoot my 270, it kicks too much. So I'm considering a 308 or 243. Which has less recoil. Thanks
I suspect the problem with recoil and your grandson is not the caliber, the .270 really doesn't have much recoil and certainly has less than a .308 I would bet the problem is that the gun does not fit him well or he is not pulling the gun into the proper place on his shoulder and if you he is shooting from a bench he will experience more recoil than he would if he was not using a bench. New shooters have a tendency not to pull a rifle tight against the shoulder which which will give them substantially more felt recoil. The .243 will have less recoil than the .308 and a bit less than the .270 but it will not be a most all big game rifle like the .270 would. I would make sure his shooting form and gun fit is right before I bought a new gun.