Judit, Quads like any fullrange electrostat or any fullrange single-driver cone speaker, are inherently time aligned. The phase alignment has to do directly with the phase shift that may occur in the single drive element. The advantages of these types of speakers goes beyond the time and phase characteristics, and into speed and coherence. Disadvantages may include narrow dispersion and intermod distortions, and possibly limited low frequency extension.
Multi-driver systems may use different techniques to create time and phase alignments, but are inherently hampered by the multiple drivers themselves. They try to simulate point source sound, but never really achieve it. In addition, the crossovers and additional drivers create as many or more problems than they solve. Advantages may include wide frequency extension, lower intermod distortion, and possibly higher power handling and SPL. Disadvantages would include crossover distortion, driver matching and overlap problems, and lack of the point source radiation pattern that they seek to simulate.
Much depends upon the system and goals you wish to achieve, and your particular sensitivity to these various disadvantages of each type. Picking the faults that you can live with is as important as picking the strong points. Nothing is perfect, and compromise is going to happen with all designs. The sound is the final arbiter, and designs are simply ways to get there. You must pick your poison.
As far as electronics matching up with these speakers, unfortunately, there is a hodge-podge approach to this in audio today. Components are designed to work with a wide range of other components, and cannot take individual speaker characteristics into account. This leads to the inevitable "synergy" discussions about what amp is best for what speaker. Some basic guidelines can help, but auditioning is really the only solution.
With the present situation, all distortions in the system will add together to give a total system distortion, as well as the same result in total system phase linearity. Some work is being done in distortion cancelling "synergy", but this is very strictly limited to certain amps and speakers that are not "mainstream" products. At least, not yet.
