CRF stands for Controlled Round Feed, PF stands for Push Feed. With a CRF action the cartridge is captured behind the extractor as soon as it comes out of the magazine box. Many claim this is more reliable, especially if you short-stroke the bolt because they believe you cannot jam a CRF action like a Winchester model 70.
Its true that if you start a cartridge into the chamber with a PF action and stop then fully retract the bolt you can create a double feed when you push it forward. It’s also true that if you do not fully retract the bolt in a CRF action far enough to engage the ejector, but enough for the bolt face to pass the rim of the next cartridge in the magazine box – which has probably moved forward under recoil – and then push the bolt forward with force, you will create a jam that is as hard to remove as an elected Senator.
The other claim is that CRF actions have more reliable extraction. I can not prove or disprove this but I can tell you that if you break the extractor on a CRF action, you best have one with you that has been fitted to your bolt. With most PF actions, installing a new extractor is relatively easy.
In the end, if you know how to work a bolt action rifle I cannot see that it really matters. For what its worth, as glamorous as the CRF action seems with its Mauser heritage, remember; a major war has never been won with a CRF action and our military’s battle rifle is a PF design. Granted, since it is a semi-auto, the user interface is not as important. And, its the user that is capable of making either a CRF or PF action fail more so than the way it was designed.