I know a guy who has a 660 in 6.5mm Mag and loves it. While the 673 comes in a 22" Barrel which is 2 inches longer than the 660 did, and if you pick the right caliber you may own a future collectible because the Laminated 660's in 6.5mm Mag and .350 Mag are much sought after. I think the 673 is the only rifle Remington makes in 6.5mm Mag, which can be hard to get shells for at a reasonable price, even if you load your own. Shells and Casings for the 6.5 are not impossible to get but they can be pricey.
The .308 should be a good, less expensive shooter in the 673 but it is the oddball calibers that get the attention in the 600's and 660's. When I was considering a 673 the .308 is the one I would have bought. Now I tend to like the Model 7 LS more than the 673. Mainly because I don't see much use for the Vented Rib. But then again, that Rib is what may make it a collectible........ who knows.