I just checked and held a .303 up next to a 7.7x58 and just eyeballing it, they don't look near enough alike to consider even trying one in the other. Different shoulder, taper, overall length and the .303 is rimmed, where the 7.7 isn't.
That said, there might be a way to get brass from one re-sized to work in the other, but I know nothing of reloading and I may be talking out of my backside. Well, actually, I /know/ I am, heh.