Okay, so at which point does this series evolve from Call of Duty to Halo? Because currently the only thing separating the two is the lack of aliens.

I think the "problem" is that the WWII shooter genre became so over-saturated just a decade ago that the companies that used to make 'em are worried that old stigma of "this is now old hat" is still around. In fact I remember when World at War came out there were people who were blasting the game just because it was a World War II shooter released one year after Modern Warfare gave the military shooter genre a much needed change up. WaW has since been "vindicated by history" for things like having a good campaign mode, being the start of the famous CoD Zombies, and for being the game that technically acts as a prequel to Treyarch's Black Ops storyline.

Lately the biggest old school throwbacks in shooters are ones modeled after 90s era shooters to some degree. Good example is the new DOOM (speaking solely about the single player here), which, like the old games, only has reloading for a single weapon (the super shotgun), minimal focus on plot, heavy focus on action that's meant to be very visceral, a hyperspace arsenal (meaning none of the "can only carry two guns" thing that became more common after Halo used it for the purposes of wanting to add a tactical element), though in a manner that's probably more akin to other old school shooters, Doomguy in the new game has higher maneuverability than he used to (now being able to double jump and mantle over ledges).