You are leaving a LOT of variables open and unknown.
The 7mm Rem Mag, 7mm STW, 28 Nosler, 7mm Wby Mag and the 300H&H, 300 WSM, 300win mag, 300 wby mag, 300 ultra mag, 30 Nosler, 30-378 wby are all capable of extremely fine accuracy.
At 250-300 yards a 300 Savage will do on deer/pronghorn.
Are you hunting deer or elk/moose?
If you had two rifles capable of producing accurate groups one in .284 dia and one in .308 dia. It is literally a toss up.