In reply to Mav.

I haven't used the other plugin, so I can't compare the two.

You can check out a live demo of Jetpack Search. I'm unsure how long that demo will be up, but it may give you a better idea of how it works.

I did want to make a small correction. Jetpack is not WordPress native. It is a third-party plugin made by Automattic. The "under the hood" part of the new search feature basically happens outside of WordPress and communicates with an API on Automattic's servers.