Though the .243 is probably fine for most deer, why not do the responsible thing and use the 7-08. If you have both, why not use the more sure bet of the two. Recoil in the 7-08 is not bad at all, so that shouldn't be an issue. They are the same case, one just gives the use of heavier bullets and more energy. Take the heavier bullets with more energy and have more confidence.
If for some reason your .243 is vastly more accurate than your 7-08, then use it. All other factors being the same, use the 7-08 with its heavier bullets.
My buddy shot a hog recencly and it dropped instantly with a .243, even though I am sure nobody will argue that is a great hog cartridge. It was all shot placement. Shooting the gun accurate is important, but I will take more bullet weight, when I can. Just makes me feel more confident.
Good hunting,
Brian