Elasticsearch will provide vastly superior search results, however it is a remote service so your community will need to make HTTP requests to it in order to index the content, and to fetch the search results. That said, the searching is faster than MySQL particularly for larger data sets.
Generally speaking, if you get to a million or two posts, you should probably switch over to ElasticSearch. Before that point, you would really just need to try it out and see if you prefer it or not. If you have a really fast server and a relatively smaller site, you may find that local MySQL searches are sufficient, and perform faster, than a remote service.