This depends on many things. Enterprise applications are normally executed within containers (for example application servers) which introduce certain abstraction for the app so that it does not care of which OS it is running in. However there are still certain OS-specific points which might matter (e.g. file path specification).
Another important thing to consider is the OS that was hosting your app before.
Anyway (if you have limited budget - otherwise it is better to perform full regression) I would recommend to test at least the cases which cover IO like
- read/write files
- privileges issues
- read/write over the network
It also makes sense to verify that you do not have performance degradation.