Update Since the time of the original posting, I've discovered that using Google's cwebp compressor shows dramatically improved compression over ImageMagik 6.7.8, which is what powered my initial tests. This is especially true for images with transparency when compared to PNGs. Files using the mac version of the webp command (which uses cwebp under the hood) are about 1/4 of the size of the same file compressed with ImageMagik, and do provide a significant performance boost.
According to Google, "WebP typically acheives an average of 30% more compression than JPG" (source) with similar visual quality to a JPG. However, as you suggest, there in never such a thing as a free lunch.
Quality
Quality is largely a subjective measure, but keep in mind that you're comparing a file compressed at quality 80 with a file that doesn't have that level of compression (at least, this is what I understand from your question). Just running the default conversion without specifying a lower quality may give you slightly smaller files without loss of visible quality. 20% smaller might be a bit much of an ask, though, but it may be achievable for certain images.
convert 1.JPG 1.webp # do not specify quality
Size
In practice, it depends a lot on your settings and your source images. For example, I recently ran this command on all jpg images in a folder on a website "in the wild":
convert filename.jpg -quality 80 -strip -define webp:lossless=false -define webp:method=6 filename.webp
The convert command on this particular server is powered by ImageMagick 6.7.8. Some files were dramatically smaller compared to the original JPGs, while others were actually larger. Overall, after running that command, the total file sizes of all JPG images was 49MB, while the total file size of all WebP images was 29MB. That's a pretty good savings, however, when I ran ImageMagick's JPG compression, it was even better:
convert filename.jpg -sampling-factor 4:2:0 -strip -quality 80 -interlace JPEG filename-new.jpg;
The size of all new jpgs in the directory was 21MB. Both are set to compress at quality 80, but the jpg compression appears to be better. This may have to do with some compression already on my set of test images and how that interacts with the WebP conversion process.
As I found, file sizes can even grow, usually if you are converting between lossy and lossless images. On the FAQ page linked above, Google claims: "this is mainly due to the colorspace difference (YUV420 vs ARGB) and the conversion between these."
tl;dr: In the wild, it may or may not improve file size depending on the type of images, if/how the source file was compressed, and what quality you set for the WebP. Visible degradation is harder thing to measure, but try setting a higher quality, or without specifying a quality at all.
