Large rifle primers DO have thicker cups, and a higher anvil-to-bottom of primer cup dimension. The also have a larger amount of primer explosive. The bigger primer mixture makes for a much hotter primer, and the difference in dimension makes for "high primers" where it is not fully seated to below the case head.
All the right reasons for NOT using LR primers in LP cartridges!
The late great Elmer Keith wrote and showed pictures of his blownup .44 Special SAA revolver. The loads were heavy, but not excessive. Analysis showed that simultaneous detonation of high primers in adjacent chambers blew the cylinder up. Firing recoil slammed the primers against the recoil shield and set them off. I've personnaly had this happen in a .45 Colt Ruger Blackhawk and it startled the bejeezus outta me!
Use the proper LP primers, PLEEZE!