The Model 12s that I'm familiar with were usually in the target and precision category and had longer barrels and a better selection of stocks and are built for target shooting.
Model 10s were more the short action working guns and an occasional Law Enforcement models. As far as I know, Savage doesn't do any additional magic on the barrels, although they do offer SS barrels on some of the Model 12s. I have never had a Savage factory barrel that shot poorly, and I have had 9 Savage factory barrels, all 0.3% carbon steel.
Both model 12 and model 10s come with bolt releases on the right side top or in front of the trigger guard. There are more replacement stock options for the top bolt release lever, if you are interested in changing stocks.
Some of the target models only come in single shot versions. The model 12s with the LR designation seem to have the precision target trigger (red blade), but the 6.5mm CM LRP I have has a right side target action with the left side solid (to add extra rigidity, I think) but has a detachable mag. The LRPV has a single shot action on the left side and has to be single loaded.
My LPR has a .3% carbon steel 26-inch barrel.
My buddy's LRPV in .223 has a stainless steel 26-inch barrel. Both have HS Precision stocks.
The long term average group sizes between my 12 FV .223 and his LRPV .223 are within 0.010 inches of each other, probably more due to a slightly different selection of bullets and 'shooter induced variation' than barrel accuracy.
Several of the newer precision Savages offerings have MDT aluminum chassis that some think look like a plumbers nightmare but I think they are intended to provide more rigidity and more adjustability, therefore, slightly better accuracy for individual shooters who are larger or smaller than 'standard'.
I have put MDT Chassis on four of my Savage rifles, two on model 12 FVs and they are much more rigid than the standard Savage stocks and they have improved my accuracy by about 13 to 22% depending on the caliber. The heavier caliber improved more, I guess because the heavier recoil needed the extra rigidity more to maintain accuracy.
I have not messed with my HS Precision stock on my 6.5mm CM model 12 LRP yet.