I'm not sure this is an apples-to-apples question. 243 is a good kid starter deer gun for sure assuming they are a good shot but the 7mm-08 is a significantly more powerful gun. We own 3 243s but only because I have 3 sons and they each started with 243. However, they've all moved on to 270, 280, and 308.
Bottom line. 7mm-08 does not have significantly more recoil than 243 (maybe less depending on the gun) but has a lot more killing power. No question for me at all.