Like you already know, this rifle could be a real shooter as most Brownings are. The .222 is an accurate round with a long and distinguished benchrest background.... more than suitable for varminting and prediator work. I wouldn't rule it out especially if you intend on handloading. The .308 would work well for what you want. Your gun ... your decision.
Still Learnin' as I go!
NRA Life Member