CrunchGear reports that the On Demand version of Rainbow Six Vegas 2 is incompatible with the retail version. When attempting to play a cooperative session over Xbox Live, the game returned an error asking that players insert the Rainbow Six Vegas 2 disc. This error occurred regardless of who hosted the match.
A call made to customer support later revealed that this is apparently a problem with several older titles. Additionally, users on the LEGO Rock Band forum report that the On Demand version of the title doesn't allow songs to be exported to other versions of Rock Band. This is understandable given that On Demand games have no manual (and thus no export code), though Harmonix notes it is "looking into" the issue.
The moral of the story, as noted by Co-Optimus: If you're planning to pick up an XBL On Demand title in order to play online with someone that has the retail version, do some research first.