Searching a directory tends to provide better results, since you can subset the search to the specific categories you are interested. Since Web sites have already been assigned to appropriate categories, there is less chance that you'll come up with irrelevant hits. However, you may also miss some relevant web sites searching a directory, because they haven't been registered. Search Engines will find many sites, but you are more likely to get irrelevant hits. Use both a search engine and a directory.
Search engines have different strengths and weaknesses.
Good research will use several search engines for the same query. Because the competition among search engines is so fierce, each is constantly adding new features. Check back on search sites to see what is new, and if the new features will help you on your search. Each search engine has its own search syntax and search options. Make sure you understand how to structure the search for that search site.