Search Engines

Because search engines don't organize results based on their subject, you may get results that have little to nothing to do with your request.
Google uses a ranking system based on clicks. The links that get the most clicks in relation to certain searches are tossed to the top. Ranking is based on popularity, but not necessarily accuracy.
Ranking can be purchased or forged giving false relevance to web pages. Ranking is also impacted by your search history and browser settings.

Library Databases

Are organized and often grouped by subjects (such as English, History, or Psychology) making it easier to find an appropriate database for your search.
You have more control over your results by applying filters for full text, date ranges, and more. This means you'll get fewer results but they will be more relevant to your topic.