Hello: I had several .303 Savage rifles, still have one, and all were fired by me with .308", 150 grain fmj bullets. Accuracy was fine, from which I infer that barrell groove diameter is nominally .308". Also, I have some Remington and Winchester factory loads which have bullets measuring .308" diameter. I infer from this information that .303 Savage does require .308" bullets.
Case capacity of .303 Savage brass is nominally 7% greater than that of 30-30 Winchester brass, and maximum pressure ratings are nominally the same. My reloaded brass base diameter when measured after firing was nominally the same as factory loaded brass, which is an empirical indicator of maximum firing pressure. My reloads were 36 grains of Accurate Arms 2520.