Being a reloader I have to approach this from a bullet selection point of view. I have never hunted with a 243 but started reloading for 7mag back in 1972. I'm not advocating a magnum rifle.
There appears to me to be very few suitable bullets for 6mm, 90gr, 100gr, and 105 grain would seem adequate for whitetail and a perfect shot at a mule deer
The offerings in 7mm include 120gr, 130gr, 140gr, 145gr, 150gr, 160gr, and 175gr in various types, including spitzer sp, spitzer btsp, a 140gr trophy bonded bear claw, 160gr trophy bonded bear claw.
Here where I live, there are more species to hunt, whitetailed deer, antelope, mule deer, and elk, along with mountain goat, Big Horn sheep and moose.
This data seems to indicated that unless you only going to hunt Pronghorned Antelope, and white tail deer, the 243 seems rather limiting to me. I know hunters can and do use 243 on Mulies, but again you may have to pass on a quartering shot that would be available to 7mm-08. oh, and while 7-08 has been used successful on Moose I think you need real confidence in your ability to take a moose with it.
All together I believe that the 7-08 is more versatile and efficient choice IMO.