As a battle rifle a reliable action must:
1) be loaded easily without jamming (method at that time was stripper clips)
2) remove a cartridge from the magazine and push it into the chamber without misfeeding,
3) not blow up when you fire it,
4) extract the empty case from the action quickly,
5) do all of the above over and over without breaking parts.
I figure all three rifles do #'s 3, 4, and 5 well enough without one having an advantage over the other. All three rifles (in original military chamberings and conditions) are tough and can take all kinds of abuse before breaking.
I think the area's where the rifles start making a distiction from each other are in #1 and #2 the loading and feeding area's.
Both the Mosin and the Lee use rimmed cartridges and suffer for it. I've found my mosin to be a ##### to load with a stripper clip (and that's with good stripper clips too). But when the magazine is loaded the magazine cut off stops the rimmed cartridges from binding when the cartridge is stripped from the magazine. The Lee action is a bit easier to load (but not much), and if the stripper clip is loaded incorrectly then you can have the dreaded rim jamb.
My vote has to go for the Mauser action, since it uses a rimless cartridge and doesn't have any feeding or loading issues. The stripper clips work as slick as snot and there are no rims, so no rim jambs.
Of course, if it was WW2 and I had a choice of what rifle I was to carry I'd immediately yell GIVE ME THAT LEE ENFIELD, because without a doubt it was the best bolt action battle rifle of WW2
