Well you didn't specify what 7mm caliber you are specifically speaking. If it is the 7mm Rem Mag, it would be good for hunting to 400yrds and hard on the shoulder for strictly paper punching unless of course you have a muzzle break. Even with that, multiple round consecutively will be limited to barrel heat and having to let cool down will make target shooting long and frustrating after awhile. Now if you stretch that target out to 700 to 1000 yards then the 7mm Rem Mag has its benefits.
If it is a 7mm-08 then you have something, but I'm guessing the latter. So with that said the 223 would be a great paper puncher and varmint round. It is very capable of taking game to 400yrds but moving into the deer size game, you are starting to limit your self to its potential for a successful harvest. This is an optimum caliber for varmints to the size of coyote at that distance and a little beyond, but not by much IMHO.
So let's look at the 243. You will use 20 grains more powder than the 223, but 20 to 30 grains less than the 7mm Rem Mag. You have bullets that can be shot from 0-400 yards that are very devastating on deer size game, and explosive on varmints to 800yrds. Using an 87 to 107(1:8 twist or less required) grain bullet will both punch paper effectively at 400 yards but out to 1000yrds(100-107grn bullet). The 87 to 95grn bullet will do wonders to anything varmint, paper, and deer to 400yrds. This is just my opinion of course. Not to mention you can save money on reloading and spend about the same as non-military 223 ammo if you have to buy factory ammo.
Tank