I think the 7-08 is the best (or equal any number of other) all-around big game cartridge for North American hunting but for deer it's got nothing on the 243. The 243 is more than enough and any more just ends up in the tree on the other side.
The 7-08 has more recoil and, for deer, its just more recoil. It's no more effective.
If someone had a 7-08 I wouldn't tell them to buy a 243 instead and if they wanted to hunt moose too, I wouldn't recommend a 243 but, for deer, its unbeatable.
The 243 also has a distinct advantage if you add "and smaller" on the "deer" equation. A 7-08 will certainly kill "and smaller" but certainly with more recoil fatigue than a 243.