Sturm's comment about primer brands is correct. I currently use Federal 150's in the .45. In the past I found the CCI primers took real effort to push in and the Autoprime indented them noticeably on the bottom. That put me off CCI primers, so the ones I still have are 20 years old. They may have fixed the problem in the interim. I don't notice any difference in insertion pressure between the Federal the Winchester large pistol primers.
You don't need to clean primer pockets for a pistol cartridge. The progressive loaders, like Dillon's, all knock out the primer at the sizing station and move the case directly to the priming station. No cleaning stop. Dillon claims to have done extensive testing and sees no performance difference.
I have found that deburring flashholes can improve accuracy substantially when using ball powder (AA2520 in .308, specifically) in rifles, but can't detect any difference with stick powder. Ball powder is harder to ignite, which may account for the observation. For this reason I will de-cap rifle cases as a separate operation before cleaning them, figuring it might make a difference to have that primer pocket clean if I decide to load a ball powder next time around. I haven't tested this theory—it just makes me feel better to do it this way.
For pistols you can get Dillon's primer pocket swaging tool to clean up military primer pockets. Because it swages, the case head brass flows and forms a slight crater rim around the primer pocket. This gets flattened against the breech face during firing, pushing some of the brass back where it was, so you may have to do this two or three times before things settle down. It's fast and easy, though.
For rifle, where case head squareness matters more to accuracy and where the bolt face pressures get higher, I recommend you go to Sinclair and get a Wilson case trimming tool with Wilson's primer pocket uniforming accessory. This is basically a profile cutter that cleans out either military or commercial primer pockets to maximum dimension and gives them a radiused shoulder for very easy primer insertion. Too much work for pistol, though.
Lubing the Autoprime matters. I have read at least one lengthy thread complaining about wear. I use a boron nitride grease packaged by Tamiya for model cars as Ceramic Grease. However, I think any good gun grease would probably do just fine. I’ve avoided using moly grease just to help keep my hands clean.
For rifle, I've had good luck with the K&M priming tool. It aligns the primer squarely with the base of the case before inserting it. The compound arm loses leverage as it approaches the final seat position, so you can feel the primer bottom out in the pocket before you indent it. It is a one-at-a-time device, so, again, not my first choice for pistol where that priming precision isn't needed. This is a slow-fire rifle ammunition gadget.