EFFICIENCY

All being the same, I would go for the less efficient speaker. Bigger amps are normally not the quietest animals out there, and the more efficient the speaker the more likely you are to hear noise (if there is any).

Power-wise, it is unlikely that your amp will run out of steam with either speaker.

Regards
Paul

How important is this difference in the final sound quality?

Not as important as how they sound to you. Get the one which sounds better.

The impedance of 2.3 Ohms is a wee bit on the low side....this would concern me as it makes these speakers in the "harder to drive" category. Remember that this speaker will take nearly FOUR times the current of an 8 ohm load and this will definitely restrict your headroom (the dynamics your amp can handle where the amp remains below clipping). A massive amp and the more efficient speaker may help in this case.

Both are Thiel speakers,the SC6 is,I believe rated at 86db and the new 3.7 at 90db.I have heard the 3.7s through three different amps,Krell and two different Classe,one of which was mine.The SC6 I heard through an Arcam 85 amp, in a barren unfinished basement.Of course the 3.7s did sound better in the perfect listening rooms,with more power,however the 3.7s cost more than double the amount of the SC6 and the SC6 is in mint condition.

Are you just thinking out loud Pegausxls?

No one here can make purchasing decisions for you. How much better, and how much you want to spend are personal choices that only you can make.

Is there any truth to the claim that, generally speaking, the same number of Class A watts play louder, or seemingly so, than Class A/B - I hear this all the time, but don't know if it is true.