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PNG seems to be going away slowly, and the battle for image compression, especially in the JPEG area, is heating up
Google:
promotes WebP formatMozilla:
came up with "mozjpeg", and it seems like Facebook donated some money to them.
Microsoft is pushing and supporting
JPEG XR.
And there are also the
libjpeg-turbo that claims better results than Mozjpeg, and the
Independent JPEG groupSo it seems like the majority of efforts are focusing on
improving JPEGAnd just few days ago there was an announcement about yet another new compression called
BPG (Better Portable Graphics), but since the codec is proprietary, it might not take off.
So from I've seen, it seems like JPEG is probably the best option as it is being constantly improved, and together with PNG is supported by all browsers. As a comparison, WebP is only supported by Chrome and Opera.
With the disk storage prices going down, and with internet speed improving, my suggestion would be to store safely your original images, and then compress them with the best at the moment compression tool. In few years, as the compression tools improve, you can re-compress again the images. But in order to do it, you need to have your originals, otherwise compressing already compressed images will result in a very bad quality.