https://nginx.org/en/docs/http/ngx_http_auth_request_module....
To me, advantage is archtectural, that I would not have specify which parameters of request are considered or how are they processed. Disadvantage is semantic, returning 403 instead of 429. But original article states returning 403 anyway.
And also, regarding rate limiting by IP, I think it should be done for 10x-100x of single user limit, just as first line of defense. Also nginx rate limiting has notion of burst which helps filter out "smart" crawlers, which unlike users, send requests for hours.