Kakashi stomps hard. Kamui snipe is nothing more than simple teleportation so that means DURABILITY DOESN'T MATTER. Totally not a NLF at all. It simply teleports ANYTHING. It'd work on Odin's eye, it'd work on Galactus' toe, it'd work on the Beyonder's head. Add Storm to make this fair.
Joking aside, Kakashi likely wins this through BFR. If he manages to teleport War Machine to the kamui dimension, there's no way for him to get back. Since many argue that kamui is "simple teleportation" then that's unfortunate for the NLF kamui snipe fanboys because the material structure and defenses in an Iron Man armor prevent it from being teleported from him separately. That includes if kamui snipe tries to warp pieces of the armor off or if he tries to amputate limbs. It's all or nothing. If this wasn't the case, then the coterie would have teleported Tony and his armor separately or even without small pieces of his armor (since the slighest breach would have infected him with nanite tech advanced and capable enough to control Thor, Wonder Man, Hulk, Phoenix, and many other Avengers/X-Men) during Contest of Champions II, but they simply couldn't.
Kakashi will try to kamui snipe and it'll either fail, since kamui snipe dimensional rifts may be too small to fit War Machine's entire body, or it will work on War Machine's entire body/armor thus BFR'ing him. Again, teleportation could only work on Iron Man armor if it takes both Tony and the armor with. Kamui snipe isn't working on Stark tech.
However, I find it absolutely hilarious that people are saying that this is a mismatch in every way. The idea that Kakashi's susano'o can destroy or crush Rhodey's armor with brute force, despite having no physical/strength feats which backs that up, is comical. The idea that War Machine cannot hit Kakashi because of intangibility is even funnier considering the fact that Kakashi still needs to breathe and hear while intangible. The idea that Kakashi even has any counter at all whatsoever against War Machine's invisibility or intangibility tech is also pretty hilarious. I mean I don't see what's stopping War Machine from doing this:
But hey, far be it from me to annoy the Naruto fanatics of this site. Just going to keep the peace until they ban it like they did DBZ.
Anyway, Kakashi still wins.