Whenever WebP gives you file size savings bigger than 15%-20% compared to a JPEG, the savings are coming from quality degradation, not from improved compression. If you compress and optimize JPEG well, it shouldn't be far behind WebP.
You can always reduce file size of a JPEG by making a WebP that looks almost the same, but you can also do that by recompressing a JPEG to a JPEG that looks almost the same. That's just a property of all lossy codecs, and the fact that file size grows exponentially with quality, so people are always surprised how even tiny almost invisible quality degradation can change the file sizes substantially.
You can always reduce file size of a JPEG by making a WebP that looks almost the same, but you can also do that by recompressing a JPEG to a JPEG that looks almost the same. That's just a property of all lossy codecs, and the fact that file size grows exponentially with quality, so people are always surprised how even tiny almost invisible quality degradation can change the file sizes substantially.