If helpful, the error message returned in the body of the request is: "upstream connect error or disconnect/reset before headers. reset reason: connection termination" and the problem has been ongoing for about a day now
Thanks for the report. I wouldn't expect the same exact request to produce different results like this just based on using different client, but it's possible that the different clients are issuing the requests in slightly different ways perhaps, resulting in the issue. Are you able to print out the full raw HTTP request and response for each client? E.g., for curl, you can use the "-v" option to show most of this. I can't speak to what debug options are available for the other client though. Seeing the rest of that information may be helpful. Please redact the access token though.
In addition to that, can you share several more "x-dropbox-request-id" response header values for these 503 errors? (Due to some implementation details a single one isn't always sufficient for investigation.)