Have some experience w/ the BAR, and the Rem. and the BAR is definitely more reliable than the Rem. but it is a self-loader and subject to more possible feed problems, jams, etc. than a simple bolt action rifle. As for accuracy, you hear tales of super accuracy to terrible. The ones I have shot would hold about a 1.5-2" group at 100 yds and that is about all you can expect or actually need on a sporting/game type rifle.
The BOSS system on the newer versions of the BAR will help in the accuracy department, as long as you are using that particualr load. You change bullet weights, powder charge, etc. then you would have to re-adjust.
As for the change from 308 to 300 Win Mag., do not believe you could do that without some major alterations to the rifle. Bolt face of the 308 is .473 and the 300 Win Mag is .532 in diameter. In other words, an entirely different bolt and probably a whole lot of other changes would be required and doubt very seriously that Browning would do this. Obviously the barrel/chamber would be different and that would require a new barrel and the costs are already "way out of line..." Interchangeability I do not think is an option here, but if it can or has been done, perhaps others could help you out here.
Browning produces some of the world's finest firearms, but I am not a big fan of self loaders for sheer accuracy or reliability in sporting arms. Just my opinion and you know what opinions are similar to!!