Clear up a few things. First your looking for the best cartridge, not the best rifle. Two entirely different things. A 30-06 with a 165 gr bullet would be equally useful in either location. But, a 30-06 with a 24" barrel in tight cover as might be found in the east might put you at a disadvantage in handiness against a 30-06 with a 22" barrel and certainly against a 308 with an 18" barrel.
Next, the 7-08 in no way duplicates 30-06 ballistics. To do so it would have to shoot a bullet of equal B.C. and S.D. and that isn't gonna happen, advantage 30-06. A 7-08 will do a fine job on most anything you'd use a 30-06 on assuming you use a proper bullet.
I think their are several cartridges that would do equal duty in both places. Start with the 308, 7-08, 7x57, 6.5x55, 260 Rem. Confine it to deer and I'd throw in the 257 Roberts and the 250 Sav. I'd include the 25-06 except to really get what it has to ofer you'd need a 24" barrel and I'd rule that out on the east coast except as maybe a beanfield rifle.
For the rifle itself, take your pick of actions. Every action you buy can be had in a cartridge suitable for either area. My cousin has been hunting deer and elk in Oregon for a lot of years, he use's a mod 760 Rem pump in 30-06 with a 22" barrel. He does not understand he's at any kind of disadvantage. I have met people that have hunted antelope in Wyoming with a bow; what disadvantage could any rifle in any cartridge have?
But, being a gun nut the idea of a different rifle and cartridge for each area appeals to me. I don't have a wife to have to explain need to! Back east I could use several different cartridges. It would be nice to have my old Rem 660 on 250 Savage! But it was a 308 and that would be just as well. Out west, I have outgrown magnumitis so I'd stick with a standarg cartridge here also. I love my Rem 700 in 6.5x06 but you can't get it across the counter. So I'd take a good bolt action in a 280 Rem and never look back.
Of course you realize that just as there is open country you can hunt in the east, there's also wooded country you can hunt in the west. You need a whole mess of rifles in different chamberings!
Just noticed something, the origional post said east coast vrs west coast! Both coast are pretty much the same and what would work on one would work on the other. Pity!