The autocomplete suggestion solution is much better. People don't mind filling of text fields They also struggle with drop downs.
EDIT: For example the autocomplete function on http://www.salary.com as the person types in a city a drop down opens that matches all the possible matches. Then the user picks the one they need.
The reason is that the user already knows the answer to the question and can type it in. A drop down requires 1. Scanning the lines, reading and processing. 2. Figuring out if the answer provided matches that of the one in their mind. 3. Drop downs can disorient users as they try to use their scroll button to shuffle through the items but ends up moving the page, and other mishaps.