Welcome to the forum.

Classic problem of using a lighter rifle. A pound or two makes a lot of difference in recoil and the .243 is no slouch when it comes to velocity, which is a key number for recoil. I'd bet the recoil feels 'sharper' than your .270 as well. No, I don't think anything is wrong with the rifle. You can get less recoil by going to a lighter bullet, but, then it might not have enough energy for deer hunting. If you reloaded then the heavier bullets at a bit lower velocity might work better.

You can do some comparisons here.

https://www.jbmballistics.com/cgi-bin/jbmrecoil-5.1.cgi