There's a lot of slop in the use of these terms. Some manufacturers refer to quasi ribbons as "ribbons," which really is misleading. Sometimes they just say "planar," which could mean anything. Also, quasi ribbon drivers cover the gamut. You have quasi ribbons that are basically true ribbons backed by plastic -- some of the Apogee mids, for example, which consist of three ribbons with side-by-side magnets (like a true ribbon), joined together with plastic. Then you have quasi ribbons in which the foil covers most of the surface area, like Magnepan's quasi-ribbon tweeters. Finally, you have Magnepan's new quasi-ribbon woofers, or at least the ones in the 1.7, in which the foil traces aren't much wider than the wires they replaced.
Still, however they're made, quasi ribbons seem to be effective at bringing the sound closer to the true ribbon sound, by controlling more of the diaphragm area and reducing diaphragm resonances. Since it isn't possible to make a true ribbon woofer and true ribbon midranges are marginal (Apogee used them and at their best they were wonderful but they had amplifier-destroying impedances and tended to twist at levels above 100 dB SPL), they're the best that can currently be done with planar magnetic/ribbon technology.
Still, however they're made, quasi ribbons seem to be effective at bringing the sound closer to the true ribbon sound, by controlling more of the diaphragm area and reducing diaphragm resonances. Since it isn't possible to make a true ribbon woofer and true ribbon midranges are marginal (Apogee used them and at their best they were wonderful but they had amplifier-destroying impedances and tended to twist at levels above 100 dB SPL), they're the best that can currently be done with planar magnetic/ribbon technology.