First of all the disclaimer: I am a dealer for Atma-Sphere. I once owned and do think highly of the Berning amp, though I'm not a dealer for them.
The reason I did not become a dealer for Berning is that I preferred the M-60 in a side-by-side comparison in my system, driving original Quad ESL's (the "57's") and some home-brew dynamic speakers. I have heard the Berning and M-60 driving Merlin VSMs, and once again preferred the M-60. I find it to be more lively and have a richer texture, drawing me more deeply into the music.
That being said, the Berning has a lot going for it. It sounds great, is very lightweight, cool-running, and can be used without a preamp. The variable output impedance control is a wonderful feature that I'd like to see on more amplifiers. Pound for pound, the little Berning is more than likely the best amplifier made.
The Atma-Sphere M-60 does require periodic rebiasing, but that takes about one minute and the only tool required is a screwdriver. You also need to observe the turn-on switch sequence, so it's a bit less user-friendly if non-audiophile family members will be operating it. While the M-60 can accept single-ended inputs, it sounds best with balanced inputs (though in the side-by-side comparison I mention above I used single-ended inputs because at the time I didn't have a balanced preamp). Note that you can also run the Atma-Spheres with less than the full tube complement, reducing the heat output and still sounding excellent (and maybe even better?) with a high-impedance speaker like your Coincidents.
I have the impression that the Berning is comfortable with a wide range of loudspeaker impedances (the variable output impedance helps here), but the Atma-Sphere M-60's don't like speakers with impedances below 8 ohms unless the impedance curve is smooth and the efficiency fairly high.
The Berning is a very fine-sounding amplifier and offers an excellent collection of qualities at a very reasonable price. Sonically it's probably among the top 10% of amps in its general power and price range. Given appropriate loudspeaker matching (such as your Super Eclipses), the Atma-Sphere M-60 is the most musically engaging amp that I have heard in its general power and price range (the 27-watt, 845-tubed deHavilland SET is also excellent, though I don't sell it). At that which they do well - which is lifelike timbres and textures, engaging liveliness, and rich inner harmonic detail - the Atma-Spheres are truly superb.
But remember I'm a dealer, fin on my back, toothy grin and outstretched hand...
Duke