Is WAAS Accuracy Superior To ILS?

[Badmachine]

Does WAAS generate more accurate position information?

"Raytheon, a WAAS contractor, measured horizontal accuracy at three meters and vertical accuracy at four meters. By comparison, a Cat III ILS is accurate only to 7.6 meters in both planes at the middle marker."

Replacing the ILS: the Wide-Area Augmentation System (WAAS) will provide ILS-like accuracy with GPS. Can it replace the familiar ground-based system on which we depend?(Instrument Landing System) | Article from Aviation Safety | HighBeam Research

If this is true, why is WAAS not deemed sufficient for all Cat III approaches?