Having shot and owned both, I would get a 7-08 for your daughter. I got one for my grandson. I got a Savage 11FYCAK in 7-08 with a detachable magazine and adjustable muzzlebrake. With the muzzlebrake open, recoil is about like shooting a .223.
The difference in recoil between the .243 with 100 gr bullets and the 7-08 with 120 or 139 gr bullets is minimal. And although the .243 is a fine deer cartridge, the 7-08 will do anything the .243 can do and a bit more.