I like to think they exist in the same shared universe as other doom mod characters. Pvt Stone's custom level has guest appearances from Magwell and Eraserguy, there's a painting of Typhon on the wall as well as an ad for Dick Danger and DRLA water. The Artificer from Combined_Arms even shows up too, if you're quick enough to find him.
As for who would win in a fight, I'd say whoever the player is controlling lol