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MNG is the "official" animated version. APNG was rejected as an official extension. However, APNG is backwards compatible with PNG, a static image is displayed instead of an animated one in browsers that don't support it, and it also supported by more browsers. Firefox 3+ and Opera 9.5+ support APNG, but only Konqueror currently supports MNG out of the box.
Plus, it runs on the most platforms; Windows, OS X, Linux, Solaris, FreeBSD, Symbian* and Windows Mobile*; and it's just vanilla HTML, JS and SVG zipped up.
*Once Opera Mobile 9.5 ships.