PNG and JPEG2000 standards aren't in competition any more than GIF and JPG/JFIF are. These newer formats were created in part to replace the older ones: PNG to replace GIF and JP2 to replace the JPG. Consequently, it should not be surprising to find that the PNG format excels in those applications where GIF's were used while JP2 provides superior results in those applications where JPGs were used.
A more appropriate evaluation of the JP2 format can be made by comparing the results of lossy JPG and lossy JP2 files. A JP2 file with a quality factor of 15 is quite usable while a JPG with the same quality factor for most purposes is not.
While it is still true that the costs of storage are continuing to drop, storage is still a finite resource that costs money. There are many business related applications that require gigabyte and terabyte storage requirements of image, video and other data. Moreover, huge, cheap, data stores are of little value if data's related resources are expensive. Bandwidth is certainly often one of these as are power and hardware. Satellite TV, MP3, the Web, and other consumer electronic applications all benefit from the effective increase in bandwidth, reduced power consumption, and cheaper hardware afforded by data compression. All these applications (and more) will see benefits from JP2 and other wavelet based compression schemes.