Hi Steve,
Honestly, either approach can work fine. The biggest advantage though of the (new) DSpace 7 REST API is that it provides the capabilities to perform
any action in DSpace (in other words, anything you can do from the DSpace User Interface can also be done via the DSpace REST API). SWORD, on the other hand, is a protocol for *submission/deposit* actions only (see
swordapp.org). So, SWORD cannot do things like update existing objects/files in the system, move things around between Collections, delete objects, etc etc.
So, if your application is only concerned about depositing new content into DSpace, then either SWORD or the REST API will work fine (it's really a matter of your preference). But, if you need to do more than that, you are better off using the REST API.
If you have further questions, let us know on this list.
Tim