Search engines index the Web in a fundamentally different way from directories. Search engines don't wait for sites to come to them. They are out "crawling" the Web every day, looking for new sites and adding them to their databases.
Even so, each search engine is only able to crawl over a portion of the Web. For various reasons, large chunks of the Web are invisible or inaccessible to search engines at any particular time.
To get a more complete picture of the Web-based information on your topic, you have to use more than one search engine.
Advantages of using search engines include:
Currency. Because sites don't have to wait to be evaluated by human editors, they appear in search engines faster than they will in directories. As soon as a search engine finds a new site, it's added to the database.
Specificity. You can get very specific when using a search engine. This makes search engines good tools to use if you're looking for very narrow or obscure topics.
Considerations to bear in mind:
Use more than one search engine if you want a more complete view of the information on your topic.
Make sure your keywords are well-chosen. As with any search in any electronic database, your search is only as good as your keywords.
No evaluation. Search engines are not selective, and don't perform any evaluation of the quality of a web site. So if you want evaluation, use a directory instead.
Search engines are made for searching, not browsing. If you want to browse, use a directory.
It takes practice to learn how to use a search engine well. Find the support or help page, if there is one, and start using the tips you find for a more efficient search.