ANATHANG RIMLESS WUD BEA DANDY...............  
 
Rimless is a must,those are the best shooters i got.   
  
  
 
 Nef -17 mach2 sportster  17 hmr sportster  22 versa pac barrel  22 mag sportster  30 carbine  30-30   308  308x444 improved  357 max talo trapper  35 whelen  (3)38-55  20"44 mag compact  .410/444 slug gun  45 colt carbine  32"45-70  32"45-120  500 s&w. 50-70 govt. BPCR  smokeless 45 cal. muzzleloader   stainless 50 huntsman  blued 50 huntsman  20 ga.slug  12 ga. tracker 2 slug gun  camo 12 ga. 3 1/2 inch  topper 158's 410,20,16,12 ga. I will take all those awful, inaccurate rimmed guns off your hands, since they do not shoot worth a darn. Yep, I will take them all and leave you the 30 carbine, 308, Whelen front loaders and shotguns...wait, the shotguns have rims too. 
Seriously - If you are having issues with your rimmed cases, do not load them so heavy and then neck size them so they head space on the shoulder.....OR  you can adjust your dies so it just bumps back the shoulder enough to chamber, so it still head spaces off the shoulder. Of course you can not do that with a straight case, you are stuck shooting them straight up, but if you do not have a rim, you need to head space off the case mouth. Head spacing off the mouth, does not make your most accurate loads. 
Rimless or rimmed, should not make any difference in accuracy. I happen to prefer a rimmed case for a single shot, break action gun but am not opposed to a rimless case. More than likely, if it were not that rimmed cases have trouble functioning reliably in bolt actions and semi/auto actions we would not have rimless cases at all. The rimmed case is stronger in the head section due to more brass there and extraction is easier to handle, but they donot funtion in bolts and certainly not auto actions very well. 
Good Luck and Good Shooting