I've been viewing, editing, and storing digital images since before digital cameras were common -- I've used GIF, JPEG, TIFF, PNG, and a few other now-obsolete formats.
GIF has been mainly relegated to animated images, because nearly any other compressed format produces smaller files (but only GIF has the ability to display multiple frames sequentially, even loop the display, built into the format spec). TIFF is mainly used for images to be stored in documents like PDF or word processor files, and PNG is the "new kid on the block" with exceptionally high efficiency and lossless compression (at least up to some point).
So, PNG is clearly superior to JPEG, both in terms of preserving image quality, and in actual compression level -- yet digital cameras seem to either save only in JPEG or give a choice of some uncompressed RAW format, with or without simultaneous JPEG.
Why haven't cameras adopted the superior PNG compression technology, which would fit more, higher quality images on a memory card and largely (if not completely) eliminate the need for dual-format storage?