Basically from what I have seen of WebP it's a joke. It may or may not be better than JPEG. We don't really know yet. The people who have done the test methodology obviously don't have image compression background.
(ADD : okay, maybe "it's a joke" is a bit harsh. The material that I linked to ostensibly showing its superiority was in fact a joke. A bad joke. But the format itself is sort of okay. I like WebP-lossless much better than WebP-lossy).
If you would like to learn how to present a lossy image compressor's performance, it should be something like these :
eg. you need to work on a good corpus of source images, you need to study various bit rates, you need to use perceptual quality metrics, etc. Unfortunately there is not a standardized way to do this, so you have to present a bunch of things (I suggest MS-SSIM-SCIELAB but that is nonstandard).
Furthermore, the question "is it better than JPEG" is the wrong question. Of course you can make an image format that's better than JPEG. JPEG is 20-30 years old. The question is : is it better than other lossy image formats we could make. It's like if I published a new sort algorithm and showed how much better it was than bubblesort. Mkay. How does it do vs things that are actually state of the art? DLI ? ADCTC ? Why should we like your image compressor that beats JPEG better than any of the other ones? You need to show some data points for software complexity, speed, and memory use.
As for the VP8 format itself, I suspect it is slightly better than JPEG, but this is a little more subtle than people think. So far as I can tell the people in the Google study were using a JPEG with perceptual quantization matrices and then measuring PSNR. That's a big "image compression 101" mistake. The thing about JPEG is that it is actually very well tuned to the human visual system (*1); that tuning of course actually hurts PSNR. So it's very easy to beat JPEG in terms of PSNR/RMSE but in fact make output that looks worse. (this is the case with JPEG-XR / HD-PHOTO for example, and sometimes with JPEG2000 ). At the moment the VP8 codec is not visually tuned, but some day it could be, and when it eventually is, I'm sure it could beat JPEG.
That's the advantage of VP8 over JPEG - there's a decent amount of flexibility in the code stream, which means you can make an optimizing encoder that targets perceptual metrics. This is also what makes x264 so good; I don't think Dark Shikari actually realizes this, but the really great thing about the predictors in the H264 I frames is not that they help quality inherently, it's that they give you flexibility in the encoder. That is, for example, if you are targetting RMSE and you don't do trellis quantization, then predictors are not a very big win at all. They only become a big win when you let your encoder do RDO and start making decisions about throwing away coefficients and variable quantization, because then the predictors give you different residual shapes, which give you different types of error after transform and quantization. That is, it lets the encoder choose what the error looks like, and if your encoder knows what kinds of errors look better, that is very strong. (it's also good just when targetting RMSE if you do RDO, because it lets the encoder choose residual shapes which are easier to code in an R/D sense with your particular transform/backend coder).
My first question when somebody says they can beat JPEG is "did you try the trivial improvements to JPEG first?". First of all, even with the normal JPEG code stream you can do a better encoder. You can do quantization matrix optimization (DCTune), you can do "trellis quantization" (thresholding output coefficients to improve R/D), you can sample chroma in various ways. With the standard code stream, in the decoder you can do things like deblocking filters and luma-aided chroma upsample. You should of course also use a good quality JPEG Encoder such as "JPEG Wizard" and a lossless JPEG compressor ( also here ). (PAQ8PX, Stuffit 14, and PackJPG all work by decoding the JPEG then re-encoding it with a new entropy encoder, so they are equivalent to replacing the JPEG entropy coder with a modern one).
(BTW this is sort of off topic, but note that the above "good JPEG" is still lagging behind what a modern JPEG would be like. Modern JPEG would have a new context/arithmetic entropy coder, an RDO bit allocation, perceptual quality metric, per-block variable quantization, optional 16x16 blocks (and maybe 16x8,8x16), maybe a per-image color matrix, an in-loop deblocker, perhaps a deringing filter. You might want a tiny bit more encoder choice, so maybe a few prediction modes or something else (maybe an alternative transform to choose, like a 45 degree rotated directional DCT or something, you could do per-region quantization matrices, etc).)
BTW I'd like to see people stop showing Luma-only SSIM results for images that were compressed in color. If you are going to show only luma SSIM results, then you need to compress the images as grayscale. The various image formats do not treat color the same way and do not allocate bits the same way, so you are basically favoring the algorithms that give less bits to chroma when you show Y results for color image compressions.
In terms of the web, it makes a lot more sense to me to use a lossless recompressor that doesn't decode the JPEG and re-encode it. That causes pointless damage to the pixels. Better to leave the DCT coefficients alone, maybe threshold a few to zero, recompress with a new entropy coder, and then when the client receives it, turn it back into regular JPEG. That way people get to still work with JPEGs that they know and love.
This just smells all over of an ill-conceived pointless idea which frankly is getting a lot more attention than it deserves just because it has the Google name on it. One thing we don't need is more pointless image formats which are neither feature rich nor big improvements in quality which make users say "meh". JPEG2000 and HD-Photo have already fucked that up and created yet more of a Babel of file types.
(footnote *1 : actually something that needs to be done is JPEG needs to be re-tuned for modern viewing conditions; when it was tweaked we were on CRT's at much lower res, now we're on LCD's with much smaller pixels, they need to do all that threshold of detection testing again and make a new quantization matrix. Also, the 8x8 block size is too small for modern image sizes, so we really should have 16x16 visual quantization coefficients).