Neither of them give you what you want by themselves; additional processing is required to get it into the format you want. The .mbox route is probably easier for your use-case because it gives you the complete dataset, and you don't have to write a client that makes several API calls.
Luckily the .mbox format has parsers in many languages that allow you to navigate its structure (four random examples: [2][3][4][5]), Python's in their standard lib, so you can do a simple script like this one, [6], and modifying it slightly to pull the data you need out.
[1] https://support.google.com/accounts/answer/3024190?hl=en [2] https://docs.python.org/3.6/library/mailbox.html [3] http://search.cpan.org/~dcoppit/Mail-Mbox-MessageParser-1.51... [4] https://github.com/robertklep/node-mbox [5] https://github.com/bthomson/mbox [6] https://gist.github.com/davidpelayo/139db134ca2337e966bb