Well, thanx kazakore, I had to chose something, so in the end, I’ve bought the Matrix M-Stage - I’ve just received it, and indeed, it perfectly feeds my DT880 600Ohms, it’s a must-have, cheap, silent hardware, and looks very reliable. I didn’t tested all things with a more clinical approach, but for now, I’m more and more satisfied. It’s not a “sonic orgasm”, of course, indeed there’s no big boost on the bass territory. But the precision, the neutral response, and the finesse in the overall sound reproduction is just what I want and what I need for my daily works.
Glad to hear you’re happy with your purchases 
I take it from that you did find it a little weak/quiet without the dedicated headphone amp then?
It is highly hardware dependent ; when I plug my dt880 headphones on some jacks i.e. my Galaxy tab jack for example, I can hear something of course, but I need to turn the knobs to the max… And the sound needs more of… everything, to be usable in a mixing / mastering phase. On some computers I don’t have to put everything to the max, for example, when I have a ALC887-like realtek chipset, that have automatic “impedance sensing” and jack detect techniques so the chipset “tries” do do something to raise the volume, so in this situation the volume is correct but… there’s big a problem, the overall sound quality isn’t there at all : even if the volume is raised, the result is flat & poor, clearly there’s a true lack of punch, warmth & crispness, even with 96KHz 24 bits rendering, some bass frequencies are unclearly reproduced (I can hear lots of “garbage” and unprecise pan positionning), so even with a nice chipset, I can’t rely too much on the dt880 headphones then. So, the M-Stage + DT880 combo seems necessary in my situation, it should give me with my headphones an audio experience that is “similar” to the one I could expect with some external quality speakers - in the end that exactly what I want. Anyway I shouldn’t totally expect miracles from all this ; I think that a successfull mix also comes from the DR managment, so maybe sould I also try for example a K-metering system with this new combo.