Both formats of advertising work in different parts of the sales funnel.
Display Advertising: Display advertising is used to generate awareness and create interest in a particular audience segment. That’s why it’s cheaper than search advertising.
Google and Facebook both have display advertising formats, but there is a huge difference between them. In terms of awareness and lead generation, Facebook (social media) display advertising is much more effective, and Google display advertising is effective in remarketing.
Search Advertising: Search advertising works at the end part of the funnel where advertisers target highly interested audience segments who are ready for conversion or sale. Only Google (and +other search engines) provide this format of advertising. This is quite an expensive but very effective form of digital advertising.