Here are some thoughts on the differences between controlled-feed bolt-actions and push-feed bolt actions, and the importance thereof to shooters.
Controlled feed refers to the system developed by Peter Paul Mauser for his Model 98 bolt-action. When the bolt is cycled, a cartridge rises up from the magazine and the extractor—that long, flat piece of metal that rides alongside the bolt—snaps onto the rim of the cartridge and holds it in a death grip on its trip into the chamber. When the round is fired, it pulls the case clear until it is kicked out of action by the ejector, a small, unattractive piece of steel that is fixed in place behind the follower and rides through a slot in the bolt face. So, controlled feed: Each round is held in place throughout the firing cycle.
Push feed was introduced by Remington in 1949 in the Model 721 (which eventually became the Model 700). Here, as a cartridge rose up out of the magazine, the bolt simply pushed it forward into the chamber without holding on to it. As the case chambers, a small unattractive clip snaps onto the rim, and pulls the case out when the round is fired. The shell is kicked clear by a spring-loaded plunger in the bolt face.
In a properly-made rifle, either system works fine.