There's a few ways it can go.
In an ideal world the big VR players will solidify the VR tech in the first couple generations, then come together to make an open platform that allows developers to easily support both HMDs.
It's a lot harder than it sounds though. The performance requirements of these systems are extremely high. Not just the processind needed to power the software, but especially the narrow tolerance for any issues with them like judder, frame drops, motion issues etc. So you can't just slap a port from one to the other together, you really have to try hard to get everything right.
This is combined with the fact that both sides are creating new technologies to push the envelope of what is possible, so it's all cutting edge hardware and software. It's not like this generation of consoles where the hardware is stuff we had in our PCs 3 years ago.
In the next couple gens both Valve/HTC and Oculus really need to focus on their technologies and give standards and universalism a back seat.
To me it's obvious that Valve wants a piece of the VR store pie, and Oculus/facebook does too. How that plays into cross-platform support is unknown.