There's absolutely no reason to think that a modern quality chrome lined barrel won't be able to provide you exactly the same accuracy as an unlined barrel. And it will do that while lasting longer and being easier to clean. That's my $0.02 on that.
175 grain bullets are about the maximum that you can stabilize in a 1 in 11.5" twist barrel, within the pressure limits of the AR type 308. (Any hard data about chamber and port pressure limits (if they exist) would be appreciated.)
There are two main differences in .308 Winchester and 7.62x51 Nato chambers (not cartridge cases).
One: The 7.62x51 chamber specifications are looser to accommodate feeding and extraction in adverse conditions.
Two: The 7.62x51 chamber has a longer throat (that is still within specifications) primarily to reduce chamber pressures which may vary based on the origin of the ammunition.
Cartridges marked .308 Winchester will chamber and fire safely in a 7.62x51 chamber. If you plan on reloading the cases, size them using a full length small base sizing die so that they will be returned to factory specifications and feed smoothly from a magazine and into the chamber of the next gun you fire them in. Surplus 7.62x51 ammunition can be used safely in .308 Winchester chambers IF the throat is not cut to absolute minimum length.
Manufacturers have a lot of lee-way in how short or long they can cut the throat on a .308 Winchester barrel while still being within SAMMI specifications. It doesn't make sense to cut a throat long enough to accommodate 180 grain bullets in a barrel with a 1 in 12" twist. You can't normally get the velocity out of them to stabilize with that twist rate. For a rifle barrel with a 1 in 10" twist rate, they'll cut the throat to the minimum required length to allow chambering of cartridges loaded to magazine length with these longer and heavier bullets. Both of these practices have the same purpose in mind: a shorter jump to the lands generally means greater accuracy.
That's the reason that .308 Winchester chambers are tighter, shorter (on the order of thousandths of an inch), and have shorter throats. It's accuracy potential. Sporting rifles are expected to be accurate enough to kill game humanely with a well placed shot and win matches. Military rifles are generally just made to be able to hit a man sized target at a minimum range specified by the armed force in question. Humane kills aren't on their list of concerns. Also, sporting rifles are not chambered with the possibility in mind of having to endure long strings of full automatic fire, or having to fire ammunition mass-produced at a possibly foreign military arsenal, especially in a fouled chamber.
If a 7.62x51 marked cartridge won't chamber in your .308 Winchester marked barrel, and you're really insistent on firing it:
Get out your seating die, and push the bullet on that 7.62x51 cartridge in a few thousandths. Military shooting teams have been known to do this for use in service rifle competitions, but it has more to do with breaking the sealant used between the bullet and case mouth in order to get more uniform neck tension on issued ammunition.
Thank you for reading.