They tried Sony and Microsoft last generation. Panzer Dragoon Orta, Shenmue II, Virtua Fighter 4, Shinobi, GunValkyrie, SEGA Sports titles, JSRF, Otogi 1 and 2, Rez, Phantasy Star Universe, Shining Force Neo, Yakuza 1 and 2... While some of those games were commercial hits, most didn't sell well. And of the ones that did sell well, most sold best in Japan.
SEGA's bread and butter last generation was Sonic Adventure DX, Sonic Adventure 2: Battle, Sonic Heroes, Shadow the Hedgehog, Sonic Mega Collection, Sonic Riders, and Sonic Gems Collection. Of those, all of the multiplatform games sold best on Gamecube despite the fact that the Cube had the smallest userbase between the three systems.
SEGA needs Japan, so the Xbox 360 obviously isn't the viable choice for franchise revivals. It got some early support (Full Auto, OutRun, Condemned) simply because it was the only current generation system on the market. The Wii took off in all regions and the PS3 didn't, so the deal was sealed.
The Yakuza and Virtua Fighter franchises remain on the PS3 simply because of its controller, in my opinion.
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