Compare them.
No, really. Save a file in WebM at the highest quality, then try saving the same file as a JPG, matching the file size. The JPEG will be much, much worse. Set JPEG to the same quality, and it'll come out a whopping 66% bigger (yes, that's how percentages work to those who see 66% and are confused by the fact that it's not 40% =)
Essentially, WebM isn't just "different", it really is unequivocally "better".
Grab yourself a copy of of the WebM Photoshop format filter, and a copy of filtermeister - open any random "real" image (let's saw a raw photograph of good old' nature, or a crisp illustrator-exported vector graphic), save it to highest quality JPEG, close the file, reopen the original, save it to highest quality WebM, close the file, and then open all three.
Create two new images, copy the origina image's layer to both, and then copy the jpg layer to one, and the webm layer to the other. Invert the colors on both layers, and set their opacity to 50%. We now have a difference result. Flatten Both images, job's a good'n.
So that's the first thing we really care about: can you see any artifacting? I've had to run this test many times, My puny human eyes can't. Not without first zooming in a lot, anyway. But let's assume that this isn't enough to convince you, because what should be {127,127,127} could be {126,128,129}, right? Maybe you care about that difference. You shouldn't, but maybe you do, so let's see how strong the difference really is.
Fire up fiter meister and write a small color ramper - For all three channels (R,B,G, neither WebM nor JPEG officially support A), set up a color ramper so that if the color is off from the 127 mark, it gets stronly boosted, say fifteen fold, with a cap at 0 and 255. Now you can see the difference in how JPEG and WebM do their magic - WebM actually uses much nicer spells, with less intense differences between the original and the lossy encoded image.
This really is a fantastic image format, and long overdue. The only tarnish on its reputation is that the world hates "new" formats. Thankfully, the company that wants to push it also happens to make one of the more popular browsers. And you can be sure that the code for enabling WebM in Chrome finds its way into webkit, followed by the Mac supporting WebM. Photoshop already supports it with the download of a single file, and suddenly its future looks nice and bright - Superior image format alternative for JPG that makes super tiny files? About bloody time.
Mine's the one with the WebM filter on a USB stick attached to my key ring.