No, Xbox 360 and PS3 players cannot play against each other online. This limitation exists because both consoles operate on completely separate online ecosystems—Xbox Live for Microsoft and PlayStation Network for Sony. Games are designed to connect only within their own respective networks.
The fundamental barrier is architectural: Xbox Live and PlayStation Network use different protocols, authentication systems, and server infrastructures. During the seventh console generation, platform holders maintained strict walled gardens, and developers had no tools to bridge them.
Cross-platform play became feasible in later generations:
Unless a specific game explicitly advertises cross-play support between Xbox 360 and PS3—which none do—online multiplayer between these two consoles remains impossible.