Elastic Search allows searching by SKU, and covers settings for control over match mode, spell corrections, and autosuggestions. There are additionally covered synonyms and stop words, settings for relevance rules, and support of multilingual search (can be used for multilanguage stores).
The Advanced Search extension doesn't have an in-built search engine but uses the one set in Magento as default. The relevance of the search results mostly depends on the search engine and its setup. Advanced Search doesn’t allow the extended configuration of the engine but is able to display search results for products, category, and CMS pages in autocomplete popup and highlight the results nicely while searching.
To learn more about the functionalities of the modules, please refer to the extensions' product pages. We also offer live demos, where our support specialists will demonstrate the work of the module per your request.