CATIA is "upward compatable" which means data from lower level releases can be open and modified with higher level releases. So your customer can open and modify your R16 files with his R17 system.
But not the other way around. You will not be able to open and modify R17 or higher files with your R16 system.
However, as you probably know, your customer can use the DOWNWARD COMPATIBILITY utility program to convert their CATPart files from R17 to R16. (it's a fairly simple process.) Then you will be able to open these files. You can use these files in a limited capacity; you add new features, you can make drawings and assemblies with these files, you can even do NC programming. But you will be unable to modify the solid file, since it's history will be deleted when the DOWNWARD COMPATIBILITY is run.
If you plan to do alot of business with the customer, I strongly recommend you upgrade your system and always run the same release as your customer.