They're not really counterparts, they're still the same Andire and Xzen (sort of). It's one of those effects of that Infinite Universe Potential thing; in this case, the portal Andire and Xzen went through that led to Equestria leading to whatever the EQG universe is instead.
The only notable initial difference is that the equine halves were human halves on that Andire and Xzen.
If two Treecos met... now that I come to think about it, I'm really not sure what'd happen. Probably wouldn't be too bad, actually. They'd probably just work together.
Guess they might try to kill eachother for similar reasons to why he hasn't cloned himself yet. He wouldn't trust it. A war between two Treecos would be bloody awful.
Not entirely sure how I got onto that topic.
Hm. Yeah, not sure how that would turn out. Anyways, I could probably write a small list of the differences between EQG Universe's and Equestria's Andire and Xzen actions/traits/etc, if you'd be interested.