Gladstone, I've waited to see if you would get some comments that specifically compare the two speakers, as you requested. But, it doesn't look like there are too many people who may have had teh opportunity to compare these speakers, although Bmpnyc has helped with his comments from listening to two different systems. So, at this point I thought I might wade in with some comments about the sound of the Eidolons that you can take for what you deem them to be worth as you try to sort things out. And keep in mind that my listening bias is almost exclusively to acoustic instruments and voice.
I own Eidolons - I am biased. I think they are exceptional speakers that do a great many things extremely well. They are very neutral, very very quick (nearly as quick as the best electrostatics I've heard), and exceptionally dynamic. At the same time they are exceptionally natural and "musical". These speakers reproduce the timbre of instruments very accurately, and catch all the delicate harmonic overtone shadings that contribute so greatly to creating the illusion of listening to the real thing. They are capable of creating the most incredibly realistic soundstage of any speaker I have ever heard - laterally, vertically and in depth. Because of their incredibly even dispersion characteristics, even when listening well off-axis soundstaging and tonal balance are better than many good speakers heard on-axis. (I will admit that I place a higher premium on accurate credible soundstaging that will some listeners.)
With respect to bass reproduction, be prepared for bass response that is not emphasized or highlighted. Eidolons were designed to be very neutral top-to-bottom. They can have very deep and authoritative bass response when the recording calls for it. They also have very dynamic, agile and detailed bass reproduction. Eidolons are always "articulate." A problem I have more often encountered is with speakers that are subtly bass boosted for real world applications, and that over-drive rooms with too much inarticulate boomy bass - including some very expensive "high-end" speakers claiming flat anechoic response.
I have never heard the JM Labs, so I cannot compare. I can only share with you my impressions of the Eidolons and those characteristics in which I think the Eidolons demonstrate great strength.
Perhaps other people could share their impressions of either the Eidolons or the JM Labs independently of each other if not as compared to each other? Kindest regards,