Only one American primer maker makes the claim that their primer is "mil spec", and that is CCI. The CCI #34 and the #41 are their mil spec primers. These numbers, #34 and #41 are in fact primer numbers that I have found on military drawings.
The Tula 7.62 is sold as a "mil spec" primer. I ran a primer test with all my rifle primers and you can see the comparison here. Plus the link to the Graf's table which compares primers.
http://thefiringline.com/forums/showthread.php?t=471454&highlight=tula
Primers are made less sensitive through a combination of harder cup, anvil angles, differences in primer composition. There may be more, but those are not referenced in the popular literature.
As an idea of primer mixes, this came from a Government document. The FA70 was an old Government primer, the other mixes, I don't remember. Most were experimental, maybe all.
I know CCI standard primers have hard cups though CCI said that they fall into the commercial primer sensitivity range.
I would not use Federals, standard, magnum, match, in any mechanism with a free floating primer. Federals are the most sensitive primer on the market and the most slam firing primer ever in Garands/M1a's.
I do not recommend Winchester. The nickle plated WLR was excellent but in 1999 Winchester redesigned their line and made their primers more sensitive. There are now reports of Winchester slamfires in Garands.
I have never used Remington but hopefully others will comment.
In my opinion, go buy CCI #34's or the Tula 7.62. The Tula were a very good price and shot very well.