I believe the CCI primers use a bit thicker cup. Maybe a little more resistant to denting, if anyone is worried.
Not always, but sometimes. Certainly more resilient than, say, a Federal Match primer (which these days is unobtainium anyway).
I know this is thread necrophilia, but I think this is worth adding if it hasn't been covered already:
Using CCI #34 primers (they come in a white box) means you're using milspec primers which are designed specifically for safety in floating-pin weapons.
They're what I use in my .308 reloads for the M14s and I notice quite a difference between commercial-spec and milspec primer cup thickness/hardness. They work just fine, and I got 'em for a reasonable price, so I figure I'm ahead of the game.
-M