I agree with much that Manuel has said. In fact, his comments refer to this url...
http://www.w3.org/TR/html401/interact/forms.html#h-17.13.4
... which states:
The content type "application/x-www-form-urlencoded" is inefficient for sending large quantities of binary data or text containing non-ASCII characters. The content type "multipart/form-data" should be used for submitting forms that contain files, non-ASCII data, and binary data.
However, for me it would come down to tool/framework support.
If you get a clear idea of your users, and how they'll make use of your API, then that will help you decide. If you make the upload of files hard for your API users then they'll move away, of you'll spend a lot of time on supporting them.
Secondary to this would be the tool support YOU have for writing your API and how easy it is for your to accommodate one upload mechanism over the other.