Quadraphonic Pressings

I have heard that a Quad. pressing may sound better on conventional 2 channel cartridges, because the manufacturing and vinyl was of higher quality to meet the demands of a Quad. stylus. Comments?
Quadraphonic pressings contain specially encoded information intended for multi channel playback.

These are inferior to traditional stereo pressings because the grooves contain out of phase information that is in conflict with two channel playback.

Music from Quadraphonic pressings lack the solidity of soundstage and accuracy of instrument timbre when compared to its stereo counterpoints. There may indeed be specific recordings in Quad that sound wonderful, but an equal quality version in stereo has always proven superior in every situation I have experienced.
I still have a few CD-4 pressings, but I have not noticed them sounding better with a stereo cartridge.