It's not possible to compare the two search speeds, as the default one is using an external paid search engine source for results (swifttype.com), and ajax search pro uses your server for searching. Swifttype is of course faster, as they have a dedicated search server, which users have to pay for monthly at a certain point.
I've put the plugin into a similar container element as the original search had and fixed the HTML code in header file as well, as if was incorrectly commented.
You can also enable a “search” button on the Theme Options -> Search Text Button panel: https://i.imgur.com/sFCvOFI.pngBest,
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