It's a concept many folks have dreamed about for a long, long time; PlayStation and Xbox playing nice together across platforms for multiplayer games. While there are tons of reasons folks assume this has never worked out, one developer explains that the issue is actually as simple as technical differences between the two entities, not necessarily a long-lived rivalry.
The folks over at Gamespot recently had a chat with Tekken 7 director Katsuhiro Harada, who said he's been championing the idea of Xbox and PlayStation cross-platform multiplayer gaming for quite some time. However, Harada explained that the issue isn't so much the fact that Microsoft and Sony are supposed to be rivals so much as the different ways they handle their security measures.
As Harada puts it, most folks just assume cross-platform gaming is impossible because nobody has cracked the technicalities necessary to make it work. While that may have been part of the whole picture last generation, when the Xbox 360 and PlayStation 3 architecture were so vastly different, that doesn't seem to be an issue these days. Harada explained that he'd love to see a game like Tekken 7 played between platforms, but security protocols make it impossible.
Harada goes on to say that this is especially difficult for a fighting game like Tekken 7, as matches must be peer-to-peer to keep things even and fair. In other words, you have to be connected directly to your opponent. That's not a big issue if the players are on the same platform/network, but the security protocols for PSN and Xbox Live don't match well and would need to be altered to make it possible.
While that might sound like an easy fix, you're essentially asking one of those two entities to completely change the way they handle security protocols, which is a heck of a lot of work, top to bottom, to figure out and implement. Also, you're asking them to do this just so their customers can play alongside the customers of the competition, which is where that "rivalry" part of the equation comes into play.
It's nice to hear folks like Harada are trying, even if it doesn't sound like it's too likely to happen anytime soon. Most recently, the folks at Psyonix stated they had opened the door to do cross-platform play between Xbox One and PS4 for Rocket League, but that common ground could not be reached.
Maybe one day. Until then, you're stuck playing on your home turf.