A few thoughts. The Tikka is only offered in a long action, so there is no advantage to 308 since it would be on a long action. Of the rifles you own there isn't enough difference betweeen 30-06 and 270 to matter. Same with 7-08 and 308, as well as 7mm mag and 300 mag. You already have a lot of overlap in your collection. Adding either 270 or 308 would not help.
Truth be told it is only a very small step from 7-08 up to 338 magnum. To argue that any 2 in between is better than the other is bordering on being silly.
Either would work. I generally like a 308 better, but in this case I'd probably go 270 if you don't reload. If you do, I'd still go 308. With handloads it can do a lot. It is also cheaper/easier to load for.