I've had the m903 for a few months now. Of the three full-size headphones I've tried through the m903 amp, the only one that makes sense is the HD800. The m903 cannot drive the HE-6, and the LCD-2 (R1) sounds better off my WA6SE. With regards to the HD800, the WA6SE has the advantage of a larger soundstage, smoother sound (easier on bad recordings), and more bass impact, while the m903 has the advantage of clarity/precision (a classic difference between tube amps and ss amps). I prefer the m903 with the HD800 normally simply because I believe it brings out more of that precision that I appreciate. I use the HD800 with the WA6SE when I've had a couple drinks ;) because I don't listen as carefully to detail then and I love the amazing combination of large soundstage and solid imaging. The HD800/m903 alone would not fully satisfy anyone here I believe, but if you have a warm set-up already, this set-up gives the listener a lot of versatility. Also, I would characterize as the HD800/m903 as bass impact adequate (extension is better). Bassheads would not fancy either product.
The LCD-2s (R1) are simply not designed for the m903. I never use the combo. It sounds as if the LCD-2s (R1) are trying to be detailed cans, but they just plain are not detailed cans (relative to others in their league of course). They have a very natural sound, and for that reason I would pair it with a tube or hybrid amp to bring out its strengths. I havent heard other ss amps, but for me the LCD-2 (R1) is better suited for an amp with a more natural, warm sound signature like a tube amp.
On a side note, the m903 does lean toward the bright side as some have indicated. I have noticed that tendency, however, more when I first listened to the m903 than today. It's possible that I just acclimated to the sound.