Hi there!
At the end of the day both of these functions do the same thing, export annotations as a string. The only difference is the format that the annotations are output in.
exportAnnotations exports annotations as an XFDF string, which is the standard format for annotations in PDFs.
exportAnnotCommand exports a proprietary format that we use internally for annotations.
I recommend using exportAnnotations since it matches the PDF Standard and is easy to parse/understand/use.
Thank you!
Logan