1. When I used this method, I get a list of events that I'm attending.
https://graph.facebook.com/me/events?access_token=...
You can try it yourself, scroll to the middle of the page and click the link
Source: http://developers.facebook.com/docs/reference/api/
2. When I use this method, I get no results.
The second one is a FQL query
SELECT eid FROM event_member WHERE uid = me()
Source: http://developers.facebook.com/docs/reference/rest/fql.query/
http://developers.facebook.com/docs/reference/fql/event_member/
Shouldn't these two methods return the same results?