It's an interesting debate due to the natures of both species.
I personally see that both parties would be even in this conflict, assuming they can't use each-other for reproductive purpose (hence there might just be that showdown-stalemate as mentioned before).
Wouldn't it be scary though? If The Thing COULD assimilate and mimic a Xenomorph? Oh jeez, it was scary when it ate a dog, imagine a Xenomorph Queen .. and all those 'eggs' O.o
Assuming it could 'trick' the Xenomorphs, into believing it is one of them .. *shivers*
Kill it with fire's gonna apply to this either way I think DX
At the beginning of the 2011 movie, I remember it taking the form of a giant insect-looking thing, so it turning into a Xeno is 100% possible.
There's nothing indicating that Xenos don't have some way to detect that the creature isn't 100% Xeno, though. To think that they don't would sell them short of "perfect organism/weapon."