Capcom vs. SNK 2 launched on the Dreamcast and PS2 on the exact same day in Japan, and actually allowed players to compete with one another online, irrespective of which version they owned.
It's easy to see the logic in this; Sega had already stated it was pulling out of the console market, so allowing its Japanese user base to play against their PS2-owning friends certainly wasn't going to have a negative impact on the console's fortunes.
Sega's OpenDice framework made it all possible, and other titles included Guru Guru Onsen 2+3, which could connect to the PS2 version, Dai Guru Guru Onsen.
Sadly, this functionality didn't extend to the West. Boo.