This is more like MP3 versus one of those random codecs available for Windows 3.1 that had some big company behind it that one day got bored with codecs and now makes industrial pizza ovens. As google is a major proponent of WebP and Google is known for dropping projects and services with no notice, and the fact that webp gives very little value on the server side and webp creates objectively worse visual presentation, it would be best to consider WebP as deprecated for any new development.

edit: I would also like to note that there is no technical reason to use WebP. The only reason it is used because Google is literally bribing you with "better rankings" for using webp. In other words, it is strictly marketing-driven.