Here is the main site I use to order the Hamburg Departure Manifests - Passenger Lists of the actual list as they boarded ship at Hamburg and ordered for about 5 dollars per microfilm roll through your local Family History Center. This is what Hamburg.de is selling but at a premium price.
Hamburg Passenger Lists 1850-1934http://www.genealogienetz.de/misc/emig/ham_pass.html
Instructions on how to use:http://www.familysearch.org/Eng/Search/rg/guide/Hamburg_Pass...
The film numbers are the Family History Library microfilm numbers FHL. The lists are on rolls of microfilm, so you need to find the correct year of departure, and the ship name, otherwise you would have to run through thousand of pages on the microfilm to find your family. They also have indexes you can use.
From what I have seen Hamburg.de will find the ship for you if they can, but if you already know the ship and date, will simply copy the Hamburg List page for you which would be the same thing you get when you use the microfilms to find the ship.