Both companies worked on and sold the Dog through their respective sites, so either Warrior will need to work as a companion piece. It's pretty clear they're trying to compete in that arena, hence the alternate heads, busts, and diorama bases. They're also [supposedly] the same size, but CP can actually label theirs as 1/3 since they hold the license -- not that this is a point against P1, I think both statues will scale nicely enough.
On display compatibility, it really depends on personal preference. What I like about the Dog base is that even though it features movie references like the candles and part of a wind tunnel opening, it doesn't draw attention from the creature. Similarly, the CP retains the majority of its silhouette while still feeling like a diorama with movie references (albeit one as thick as a sub sandwich).
Here's a crummy mockup I made to compare how the Warriors might look next to the pooch. Scale isn't precise, this is more to just compare the overall look and feel of each piece. Neither looks too out of place aesthetically. If P1's didn't have the hive and egg, it would have about as much empty space as the CP, so it comes down to whether you like how they've filled out that space. I will say it would be nice if CP reduced the thickness of their base and brought the water level closer to the floor.
From what we've seen on Beesub's page, the CP Warrior bust also seems to be more in line with the Dog bust; they chopped it off mid-torso with a slimmer piece connecting it to the base. P1's bust is basically a full torso without arms emerging from the base and thus will stand a few inches taller than the Dog's. Not an important component for most people, but I'm a bust fan so I noticed it.
You know, if they just made the darn announcement we'd have much more exciting things to talk about.
