The Quad 63 has always been a great match with our M-60 and MA-1 amplifiers. The speaker has an impedance peak in the bass that is well over 40 ohms and many amplifiers, especially transistors, don't make a lot of power at that impedance. OTLs, OTOH, once you get above a certain impedance (depending on the size of the OTL) will exhibit a sort of 'constant power' characteristic, so their output power does not drop significantly in the bass.
Unlike a lot of box speakers, the Quad's impedance curve has nothing to do with either crossovers or resonant peaks. It has mostly to do with the inductance of the matching transformer and the capacitance of the panel. The result is that a constant power characteristic in the amplifier is desirable if you want to get the most out of the speaker.
see
http://www.atma-sphere.com/papers/paradigm_paper2.htmlfor more information.
With transformer-coupled tube amps, the trick is a moderate-powered amplifier that does not use a lot of negative feedback, usually set on the 8 ohm tap. With an OTL of course, you just hook it up. Since the 1950s, Quads and OTLs have always been the ideal match. The speaker is quite transparent and getting rid of the output transformer is very noticeable! Later Quads seem to be following the same path as Martin-Logan, by having very low impedances, in order to get them to work with transistors, but IMO/IME this tack never works- if you really use it with transistors it will be too bright and no bass. IOW tubes are still the ideal method with newer ESL designs but you have to use a set of ZEROs (
http://www.zeroimpedance.com) to make them work.