Pistol primers are quite different than rifle primers. Thinner metal cup so the relatively light hammer / striker impact from a pistol or revolver will still reliably ignite them. Made to handle lower pressures. The lower charge of primer compound is of lesser concern, but may not ignite slow burning rifle powders reliably. Large Rifle and Large Pistol primers differ in cup height ( primer pocket depth) too. Rifle primers are taller and fit a deeper primer pocket in the case.
Don't "try it" by substituting a large pistol primer in a rifle case for a full power rifle load because the rifle can produce pressures more than twice what a typical pistol cartridge produces. Even comparing 36,000 PSI for .44 magnum (one of the highest pressure pistol cartridges), vs 65,000 PSI for an ordinary .270 Win. shows quite a big difference.
Put a large pistol primer in a .270 standard load, and you're very likely to experience a pierced primer. Thinner primer cup and shorter so it's likely to be deep set in the rifle case, so it may back out a bit on firing and make the divot from impact of the firing pin seem "deeper" and so will blow a hole in the primer cup by cutting around the firing pin indentation. Bits of primer and powder gasses in your eyeballs could ruin your day. With a mild trail boss load or cast bullet load at mild pistol pressures, you may get away with it.
In comparison, pistol primers of the "Small" size are the same outer cup dimensions as the small rifle primers, just thinner metal cup and weaker ignition. For mild loads in rifle cartridges like the .22 Hornet, sometimes small pistol primers make an accuracy improvement and can be used safely if you know what you're doing.