Smaller files at similar quality
WebP generally compresses photographs more efficiently than JPEG, so the same picture usually comes out noticeably smaller.
That saving is the whole reason to convert, and on a page carrying many photographs it adds up to a real difference in how quickly the page loads. The gain varies with the picture: busy, detailed images benefit most, while very small or already heavily compressed images may barely change. If a particular file comes out larger than the JPEG it came from, the original was already compressed hard and is best left alone.