The algorithm for determining paincrit is decent and functioning in HvX, but I think it goes completely wack in HvH because of the nature of the injuries you get. I am not sure the exact mechanics exactly but since you get afflicted with more statuses like broken bones, internal bleeding, regular bleeding, delimbing, shrapnel, burns from incendiary rounds, flamethrowers, fire nades, etc etc could go on forever. A couple instances of damage can leave you with so many status problems that your character just keels over and begs for death. This is a large sort of the frustration of HvH to me, on top of all the other things people have been mentioning, where casual stray fire, spray and pray from across the screen, someone running and tapping you once, just leaves your character in a totally unsalvageable state. Being a medic in HvH is fruitless and beyond all hope, because people come down with every sort of status ailment known to the game and all you can do is try to get them to stop bleeding to death before they can make it to whatever side's medbay. That is, if them getting shot hasn't led to them getting beheaded, losing limbs, a giant hole for a chest, stab wounds from the victor's attempt to behead, shrapnel in every orifiice, the kind of patient you see in HvH and just shrug, with legitimately almost nothing you can do to alleviate most situations.
On top of this, the game is balanced for marines shooting at and using marine tools against xenos, and xenos clawing and using xeno tools against marines. For the most part, this is decently balanced and established. However, when you throw marines shooting and using marine tools against humans, and the humans shooting and using whatever tools they are given against marines, the balance goes completely wack, and this balance is so off IMO that the experience is detracted from because of it. I think for HvH to work, it needs serious balance considerations on par or nearly on par with the considerations given to the balance of HvX. Otherwise it's just a bunch of chimps given machine guns and told to balance their jungle conflicts with those instead of fists.