The .280AI should have a bit more case capacity and a longer neck. If you want to mag feed, though, you will lose the case capacity advantage because you will have to seat those long 180's pretty deep.
The .284 will allow you to take full advantage of available case capacity and still feed from the magazine. Based on testing I have seen with the cartridge, RL-17 would be the go to powder here. A true 9 twist will do just fine for what you want.
As for the 338-06, the 7mm does not posess a B.C advantage, though it does posess a speed advantage using comparable b.c./sd bullets.
Load the 338-06 with 250g Berger Elite Hunters (B.C. .682) and you have a combination that carries quite a bit of smackdown to 600 yards. Load it with a 225g Cutting Edge (B.C. .640) and you will have a flat shooting, hard hitting combination that will be good to around 700 yards. The downside is, that to get this level of performance you will have to load to a COAL that will require single feeding of either round.
You also have the option to sacrifice B.C. and go for all out speed. You can load a 185g Barnes TTSX to 3000+ and still be good to around 600 yards. The Barnes bullet is short enough to magazine feed.
I am getting ready for a 338-280AI build. It will have a 26" barrel and I plan to use the above mentioned bullets. I expect it to be a very good combination in a carry weight rifle.
The .284 may be more your style, though. In the end, ya gotta go with your gut feelings about what will make you happy. You can study ballistic charts and load data all you want, but keeping the fun factor in the equation is just as important. Take the fun factor away and an enjoyable pastime starts to feel more like a chore.