E7+E9 is
DAC
Portable AMP
Desktop AMP
Matrix M-Stage is:
Desktop AMP
If you're looking for amp only, I'm sure there will be a wave of head-fiers saying the M-Stage is UNDOUBTEDLY better than the E9 (without having tested both).
I however will go out on a limb and say that both are known to be quite neutral and won't color your headphones with excessive warmth or brightness, and lets the headphones themselves paint your music. The SQ should be quite close to one another, though I haven';t heard of one person having tried both. As a reference, go to the AMP A/B Comparison thread on here, so you can see how one of the very few people to one various amps and A/Bs them says how close in sound various neutral SS amps (like the E9) are to one another. Should give you a rough idea in how much one amp may be better than another.
Also, if you're on a computer and using stock soundcards, a DAC is even more important than an amp. I'd get a DAC first above anything (doesn't have to be the E7, though it's a great starter FWIR). It's been told to me but, place priority in sound like this:
Headphones
Source (DAC is a source)
Amp
Cables, and other misc items.
Also, how much are you willing to spend, what are your goals with your setup, etc. All these things can help the well knowledgeable Head-fiers help you.
I'm still upgrading myself, not because I'm unhappy, but because I need an amp to drive an Ortho, and because I wanna see what a somewhat reference DAC can do compared to my entry DAC.