If you are using third party extensions and they don't have a matching Smart Search plug-in, then Joomla's search can be pretty limited. You need to have plug-ins enabled for each component's content to appear in the results, and even then it's not always that accurate.
When searching is important, I tend to use Google's Custom Search. Ultimately, Google's algorythm is going to be vastly superior to any self-hosted PHP one since high quality search results are such a complicated thing to get right.
The main downside to using Google Custom Search is that your pages need to be indexed before they appear, rather than appearing as soon as they are published, and that you need to pay to remove the adverts.
Also, this will only work if you want users to search the site's front-end content rather than search hidden content such as a database or that content which is only available to logged in users.
There is a plug-in to add Custom Search to your site here (I have never used this so can not guarantee it works), though if you have any development knowledge, you'd probably be better writing your own module.