Apple is changing their privacy settings for iOS6 and deprecating device UUIDs (UDIDs). According to a WWDC presentation and the docs there are two replacements for the UDI
They are two different ids meant for two different purposes.
I would think that the identifierForVendor would be the one to use to do things that require the app linking to a specific user / device such as provide push notifications and updating the user's app data serverside (like their score or whatever other data is being stored for them).
The identifierForAdvertising should be used for things such as targeted advertising and also to check the effectiveness of a particular ad campaign (check to see which devices installed apps due to a particular ad).