Hi Michael,
In partial payment the original invoice amount will be available in the line item report till it is completely paid off whereas a residual payment will clear the original invoice and create a new document with the pending amount with the new date.
So ideally speaking from aging perspective partial payment is stronger than residual payment. Since in the later there is no trace of original invoice date.
Also you can refer to scn thread below for more information:
http://scn.sap.com/thread/580114
Hope this clarifies and based on this you can suggest to client to go for partial payment which has original trace of invoice date.
Hence it is difficult to say which method is better, since it depends purely on client requirement.
Regards,
Rithin