I've owned both the M50 and DT770 Pro 80 Ohm and would give the 770 a slight edge.
Advantages over the M50
More Bass - if it's too much you can always lower it with an EQ but it's better to have too much bass than too little, as boosting frequencies to compensate for a deficiency will result in distortion.
Wider Soundstage - With it's shallow earpads and tight clamping force, the M50 can feel closed-in and sometimes claustrophobic. The DT770 has excellent soundstage width for a closed headphone, which is a big benefit for music and gaming alike.
Comfort - This is the biggest advantage that the DT770 has over the M50. The M50 is an over-the-ear headphone but it is a very tight fit inside the earpads and they may squish your ears a bit if they are large like mine are. The DT770 earpads are larger and deeper, allowing my entire ear to fit inside with room to spare. The earpads are a soft velour which absorbs sweat, as opposed to the M50's pleather pads which allow sweat to collect on them. The DT770's clamping force is moderate, definitely not as tight as the M50's.
Disadvantages
Peaky Highs - The DT770 has a noticeable treble peak in the 8-10 kHz range, which results in sibilance that can get pretty annoying. This is easily fixed with an EQ. Even lowering the treble on my TV works well as most simple treble controls are centered at 10kHz. The M50 has this problem too, although it is not as pronounced.
Boomy Midbass - This is a very slight problem. There is a ~2 dB midbass hump around 125 Hz that can muddy up the bass in rock music. Too much midbass can make the bass guitar and the low end of the guitar blend together and become indistinguishable. Again, easily fixed with either an EQ or a simple bass control.
Efficiency - The DT770 Pro 80 Ohm's relatively high impedance compared to the 38-ohm M50 means that the M50 will get significantly louder. Their sensitivity ratings are similar. If you like to listen to music loud, the DT770s will require an amp to get the job done. The FiiO E11 is a great portable headphone amplifier. I'm not familiar with any full-size or desktop amps. For reference, when I am playing NBA 2K13, my TV volume is around 20 with the M50s and 40-45 with the DT770s.
Low Bass Distortion - At near maximum volume on my E11, the DT770s will distort the low end of the bass spectrum. This is a problem only with some hip-hop and dubstep songs that have an emphasized low end. I listen to a lot of rock and some metal and have found this issue to be non-existent with those songs.