The Quad 63s are great if you want fabulous transparency but have some budget constraints. They are easy to drive with most tube amplifiers; transistors will be bright and free of bass.
The big Sound Labs (I guessing- U1s? A1s?) are harder to drive, but capable of greater dynamic range and greater bandwidth, at both extremes. If set up right, there is no need for a subwoofer, a common add-on with the 63s. They are very cohesive and revealing, pretty much setting the standard for what that means in an ESL. The downside is that they need power- 200 watts is adequate if from the right amp. Usually if you have transistors, this means that you will need 600 watts so that there will be sufficient power at low frequencies (and is why a 200-watt tube amp can keep up easily with a 600 watt transistor amp on this speaker). The other downside is that the revealing nature of the speaker and the demands that it makes of the amplifier contribute to a speaker that can be very picky- and they can be underwhelming if these factors are inadequately addressed!!
The Magnaplanar 20.1 is one of the better deals in audio. It is full bandwidth like the Sound Lab, not nearly so expensive, yet nearly as revealing and capable of similar dynamic range. It is actually fairly easy to drive, despite being 4 ohms. Again 200 watts is a good amount of power to have for this speaker. Tubes and transistors are treated equally well (whereas the best results with the ESLs will be with tubes despite anything you might hear to the contrary) so you have a wider pick of amps to use with them. Being flat,, you would expect a certain 'beaminess' but this is not the case as it is not a full range speaker, but a 3-way and the tweeter is narrow. On account of the 3-way aspect, it is less cohesive than the ESLs (which are full-range devices, although the Sound Lab has a crossover to accommodate its matching transformers...) but trades some of that off by not having a step-up transformer in the signal path.
So (my recommendations) if you have a smaller room go with the Quads and some sort of tube amp. A moderate or larger room will be better for the Maggies or the Sound Labs. In all cases the speakers really should be at least 5 feet from the rear wall to realize the best results (closer will result in 'one note' bass). You can toe in the Sound Labs a bit to reduce this. If you are married to transistors, go with the Maggies (they will be smoother in the highs due to the interaction between the amp and speaker); if tubes are an option either can be used. The Sound Labs are more revealing but you will really have to have the right amp to make them happen.
Clear as mud?