Just a heads up, finally gentlemen on another forum slugged his new/latest vz2008 barrel and came out to be .308 so if you plan on shooting Russian 7.62x39 ammo which is .311/.312 out of the .308 barrel it's just something to consider
It's really a non issue, if anything a net positive, provided the chamber is properly cut for .311 bullets...
I believe US military specs for 308/30 caliber barrels is .3065 to .3095. That's a 0.003" spread, which is the same between .311 and .308. .308 bullets are allowed up to .309 diameter I believe so that's a max spread of 0.0025 from minimum chamber. Most folks that pull the bullets find Europe/Russian 7.62x39 HP running .310 to .311 and FMJ .309 to .310. Only the .311 diameter bullets could present a problem, and even then your diameter is only over 0.0005 inches (at one-tenth of one percent, 0.1%) for a .311 diameter bullet.
The primary smaller bore benefit is that Hornady 7.62x39 VMax and several other expensive 7.62x39 ammo loadings are in fact using .308 bullets. Running in a .311 barreled gun will reduce accuracy, possibly substantially and possibly even keyholing these premium loads. (And you too can reload 7.62x39 w/ the same 308 bullets you run in other 30 caliber platforms w/ no performance degradation in your .308 barreled VZ 2008.)
Secondary benefits are that tighter bores may improve bullet stabilization/accuracy, and allow for more barrel wear to occur before losing substantial accuracy with .311 Russian ammo (something to consider w/ neither chrome nor nitriding on these barrels).
Point being, until someone provides credible evidence of chamber sizing issues, which I haven't seen even mentioned, there's not a substantial reason for concern.
EDIT: Some Hornady's 7.62x39 bullets are in fact .310; others disagree. Regardless, many other US ammo manufacturers' 7.62x39 bullets are not -- and especially for reloading the Russian spec bullet selection is thin.