I compared weight, overall length, price, and availability/cost of magazines. The laminate-stock version of the GSR is just too heavy (7lbs without sling, scope, or ammo, compared to the same weight in the MVP with everything) and expensive for me to justify for myself. The extra 3.5" on the barrel is nice, and I definitely like that Jeff Cooper's training school helped design it, but those advantages are outweighed by the extra $220 and extra weight. The fact that the mags are significantly more expensive also gives the MVP the advantage.
I'm comparing each rifle to Cooper's definition of the idealized Scout Rifle, and the MVP ticks more boxes than the GSR right now, and it's cheaper to boot. Moreover, watch Nutnfancy's YouTube reviews of both rifles. Though his MVP review is on the .223 version, I don't see why it wouldn't apply to the .308. He seemed to like the MVP a whole lot more than the GSR, especially in terms of weight and accuracy.
If the price of the new (and lighter) synthetic-stock GSR is comparable to the MVP and the price of the polymer mags came down, then it would give the MVP some serious competition. I mean, I like the GSR well enough, but I just don't see enough advantage to justify the extra cost.