There won't be any online battling as Namco have reserved that for Soulcalibur IV, but they'll have leaderboards.
Soulcalibur for XBLA will also have arcade mode, training and survival. Fans maybe a little sad not to see a full blown multiplayer component but that would have been stealing some of the thunder for upcoming Soulcalibur IV. The latest iteration which does let gamers fight across the globe is coming to both Xbox360 and PS3 with a July 29th release.
Soulcalibur launched on SEGA's Dreamcast console with very high praises from both the press and fans.