For information about emigration from Bremen and it's harbor town of Bremerhaven see:
http://www.deutsche-auswanderer-datenbank.de. For information about emigration from Hamburg see:
http://linktoyourroots.hamburg.de/. It is hard to say which port was busiest when, but everything I read says way more people emigrated via Bremen than Hamburg. Unfortunately, most Bremen records were destroyed, so if you have verified that your ancestors left from there, then that will probably be a brick wall. (By the way, if you use Germans to America to get port of departure, don't trust it. According to GTA some of my ancestors left Bavaria via Gibraulter, but when I checked that against the New York Passenger List, they left from Hamburg.)