Hi,
The Objective 2 ain't a very strong amplifier, and the K702 may not hit peak performance for headphones that don't have enough headroom in power.
You may not notice a difference so subjectively, going with a stronger amplifier will likely not be something you particularly gain a noticeable sound difference from. It will be better as headphones do best with more power, and at the price, I'd seriously consider that amp he's offering.
AKGs are known to be picky with amplification, and do respond well to more power, and are also adversely affected by output impedance mismatches as well. So if you have a high output impedance amp, it may make your lower impedance headphones sound softer, beefier in bass, but also less controlled (it may be subjectively pleasing however, but objectively worse). Personally if it sounds nice, I don't care. I'll take subjectivity over objectivity, personally.
The O2 and that M-stage seem to have very low output impedance, so the change won't be that huge in terms of tonal shifts.
That M-stage is class A which brings some benefits compared to non Class A amps like the O2.
Dynamics, tactility and speed are usually a net gain with better amplification, though again, headphones don't just magically change, and again, it will be subtle. We're in a game of subtleties, and you may not even hear enough to care. Soundstage and imaging may be an improvement but that's something I don't expect much difference from with any amps, personally, and would take a severely underdriven headphone with an applied virtual surround signal like Dolby Atmos (only for 7.1/5.1 content and games), than feeding a nuclear plant of power to a headphone expecting more soundstage and imaging just due to the better amplification.
So again, in short, I'd take the M-stage simply because that O2, while clean, doesn't have any sort of real headroom. I think the K702 Annie will sound better with the M-stage, if slight.
As for DSD... I know nothing about it, and personally don't care. I'm one of those people perfectly fine with properly recorded audio at 320kbps compressed mp3. I hear the difference in going lossless, but it's subtle enough for me not to care, and the way audio is mastered is more important than the format itself to me. I'm not THAT picky about such nuances otherwise. DSD just sounds like some new form to give me clean audio, but I've been happy with audio quality since CD came about, so while DSD sounds cool and may be beneficial, it's nothing I'm invested in whatsoever.
edit:
Audeze has a good article on amplifiers/power/etc, it's REALLY worth a read (not shilling, I think it's great info that will help people understand that it's not simply about getting more volume, or that enough volume is "enough").
https://www.audeze.com/blogs/technology-and-innovation/sensitivity-impedance-and-amplifier-power
