Two very accurate hunting rifles from the shop of the David Miller Company in Tucson, Arizona. Bolt rifle barrels can be totally isolated allowing free and predictable harmonics. ARs are able to produce some pretty dang good accuracy but a bolt gun, for the most part, will be more accurate. Therefore, bolt actions tend to be more accurate.
Many bolt actions have more accuracy though and for serious target shooting a heavy barrel bolt action is the best. While they are not all wrong, they are all a long way from being entirely correct. The accuracy of these two very different rifles has a lot to do with construction and how they work, not the shooter themselves. Theoretically it should work out that way, but in the real world it just doesn't.
Also shown (above) from the Miller shop is the Marksman rifle. I have seen experienced bolt-rifle guys have great difficulty achieving the same accuracy with an AR. At top is a Miller Classic rifle, to my knowledge the most precisely built bolt-action rifle made today. All the comments made on this subject are well-considered and, by and large, correct. The American rifle has become a standard among budget guns; it is an affordable, accurate rifle family that has grown to include eight different models. If the same shooter used an AR-style rifle at range, then used a bolt action rifle in a similar caliber at the same range, 9 times out of 10 the bolt action would be more accurate. There are many match grade autoloading rifles - M1a, AR-15 etc that will shoot equal to or as good as a bolt gun.
It is also the most expensive that I am aware of. As you might guess, there is no one component that makes a rifle intrinsically accurate. The Ruger 10/22 comes with a target barrel and is worth the extra in price if you want that bit of extra accuracty in a semi-auto. Bolt-action vs. Semi-auto. What about at 100 yards? The mechanics of a bolt-action rifle are not all that complex. All these guns come with a Marksman Adjustable Trigger, cold hammer-forged barrel, Power Bedding, barrel nut, tang safety, detachable box magazine and much more. This is an article about the best bolt action rifle options. 4 Reasons You Need A Bolt Action Rifle. I will assume “regular rifle” as rifles that are not precision rifles.
There is an ongoing debate as to whether someone should purchase a semi-automatic rifle or a bolt-action rifle for long-range precision shooting. Now if we are comparing my 1941 No1 MkIII* to my AR the AR will win every single time. Almost all semi auto rifle deigns need a gas system, and that requires attaching things to the barrel that vibrate differently than the barrel, making the harmonics difficult to predict. It takes practice and focus, which a bolt rifle will let you slide on at times. It's more a matter of the comparison of apples and oranges. Bolt-action vs. Semi-auto. Some claim a certain brand of rifle is always more accurate, because it is what they own. It depends on the individual rifle, and there are so many factors that make an accurate rifle that it would take three pages to list.
Yet, the simplicity and strength leads us to expect the finest accuracy from the design. Is a bolt action any more accurate than a semi auto? Theoretically it should work out that way, but in the real world it just doesn't. Among the myriad of forms of repeating rifles, the bolt-action is among the simplest. Autoloaders also tend to go through ammo like water - and - the barrels will wear out. I see alot of other answers about the skills of the shooter, that has some part to play but it is not entirely true. The two firearms fill to vastly different roles.
Edit: What this means is that a bolt action doesn't quite have as many possible places for the process to change, making the bullet's point of impact change. In it, you will find a mix of different bolt actions that are applicable to many different shooting scenarios. I see alot of other answers about the skills of the shooter, that has some part to play but it is not entirely true.
Some tout the esoteric notion of the "inherent accuracy" of a cartridge. This is why most precision rifle competitors start with bolt-action rifles—they are just plain easier to shoot well. It depends on the individual rifle, and there are so many factors that make an accurate rifle that it would take three pages to list. But for the sake of argument, a modern bolt action rifle will be more accurate than an AR.