I have a Bergara B14 Hunter and had a Ruger American Predator in 6.5 CM. I've had multiple Ruger Hawkeye rifles in the past, but cannot comment on this specific rifle. Traditionally speaking the CRF action of the Hawkeye as well as previous versions of the Ruger 77 are noted for extreme ruggedness and reliability with accuracy more than suitable for hunting.
But when making a choice where shooters are trying to squeeze all of the accuracy they can out of a rifle the Rugers based on the 77 action are rarely in the conversation. All of the Hawkeyes I've owned or shot were 1 MOA shooters which is perfectly acceptable for hunting, but target shooters generally want more accuracy. Both the Ruger Predator and the Bergara are more accurate than any of the Hawkeyes I've shot . But I'm sure this rifle was put together with a little more care than the standard 77 rifles and would expect better accuracy. The new Ruger may well be just as accurate, maybe more so. But if I were a gambler and betting with the odds, the odds are in favor of the Bergara being more accurate.
Either barrel length is more than enough for most people. The 6.5CM takes advantage of aerodynamic bullets to retain speeds down range and only needs moderate muzzle velocity. Even a 20" barrel is fast enough to get you to 1000 yards. The 24-26" barrels are for the guys wanting to shoot beyond a mile.
If I were looking for a rifle that absolutely, positively had to function no matter how dirty or abused in order to stop a charging bear the Ruger Hawkeye would be near the top of my list and a Bergara or Rem 700 not even on the list. They are different tools for different jobs.