Interesting enough it was MS who didn't want crossplay in the 360/PS3 days
As cool as this sneak peek was, Trion can't let the finished Xbox 360 game connect to the PS3. "Microsoft won't let Sony players play against them," Rodberg said, before suggesting we change the topic to something less sensitive. Presumably the barrier is a corporate and/or technical incompatibility between the Xbox 360's Xbox Live and Sony's PS3/PSP PlayStation Network. Those services are separate enough that people who play, say,
Call of Duty on one, can't play that game against owners of the other, rival console.
I checked with Microsoft to be sure Rodberg wasn't maybe just mis-hearing them. Maybe Microsoft wanted to break the barrier too? Here's a Microsoft spokesperson saying "no," while promoting how awesome the Xbox 360's online service is: "Xbox Live delivers the best entertainment experience unmatched by anyone else, with 35 million actively engaged members. We have a high level of expectation for our game developers to ensure that all Live experiences remain top notch. Because we can't guarantee this level of quality, or control the player experience on other consoles or gaming networks, we currently do not open our network to games that allow this cross-over capability."
https://kotaku.com/i-saw-the-playstation-3-wired-to-play-against-an-xbox-3-5813740