While, yes, the Bolt Action will ultimately be more accurate, it doesn’t happen right out of the box. An AR style rifle can also be incredibly accurate. .25moa is not an unreachable goal. Many, many AR10’s & 15’s have accomplished this. However, it’s not easy or CHEAP! Same goes for the bolt gun.
First decide what your personal goal is. What is it you are doing primarily? Hunting? Target shooting in competition? For fun? And of course, what is your realistic budget? Not to mention your realistic skill level.. For instance, myself. I’ve done this a long time, and have a great deal of working knowledge. At one time I was very, very accurate. Unfortunately, I was disabled several years ago. To add to, my left eye is completely blind & my Right is heavily corrected with astigmatism. My Left arm is also completely paralyzed. Now, I can still shoot with decent accuracy. Meaning, I can HIT a man sized target at various distances. But shooting those teeny-tiny little groups on a target is no longer in my purview. It’s not part of my skillset any longer. Of course I still go for as accurate as I’m able, but Ultimate Accuracy is not the sole factor behind my choices. I’m a DIY guy. A Hobbyist gunsmith, builder. And even machining my own parts. That brings me joy. Im also a Savage loyalist. I very much like Savage 110 rifles, since I purchased my first one at age 18. My current bench gun is a Savage 10 Action with a considerable amount of money invested in it. While I “could” have built up a Custom Action like a Kelbly’s, Big Horn or Curtis had I been so inclined…. and yes, one of those are capable of better accuracy, it would do me bo good. My Savage Bench gun is more accurate than I am. My groups on paper would see no increase whether using it or a Custom, because my body no longer possess the tools to take advantage of the POTENTIAL better accuracy. And in the end I would not enjoy one of those as much as I enjoy working on Savage Actions. I enjoy making the Actions work better.
So do what you know will bring you the most joy that will meet your budget. I hope maybe that makes sense to some.