How does this compare to the Audio Technica M50x?

AS an audio engineer I can share with you these are two different headphones and I believe their respective sound strengths and weaknesses reflect their nature. Without getting into the techno babble, I will simplify this in the following manner: The Audio Technica M50x is a general headset which is good for listening to music and due its build design very good/great for gaming. The Beyerdynamic DT 770 PRO is great for audio production and more detailed listening for music and good/very good for gaming. If you are looking for a gaming headset, you can't go wrong with either, if you are looking to listen to music and want a more detailed sound or if you using them for audio production then the Beyerdynamic DT 770 PRO should be your choice.

Does the 30 ohms have the same bass output if it is connected to an amp compare with the 250 ohms?

I am looking at this 250 ohm headphone because it has a high impedance. I build a vacuum tube amplifier with a nominal impedance of 600 ohms. Although it seems to drive 32 ohm headphones, it will work better with headphones closer to 600. The high voltage changes needed to drive high impedance headphones do not carry a lot of current, but they do carry much detail. I tend to believe that high impedance headphones will be more responsive and defined than lower impedance headphones, but their hardware requirements are different. Small mobile devices don't have high voltages in them to generate signals for high impedance headphones, which is why low impedance is standardized, and even then, many devices lack the power to drive the bass on them. A dedicated amp is the extra hardware to fill out a quality signal. So even poor quality headphones can sound better when driven by the appropriate source. In the end, your headphones will not improve the sound significantly if you do not have an amplifier to back them up, though I still think higher impedance phones will result in a better sound.

Given the prices $180 for 32 ohms, $278 for 80 ohms, and $170 for 250 ohms, which one should I buy for 98% amp-less listening?

For an amp-less setup the 32 Ohm are the way to go. Yes you can use the 80 Ohms non-amp'd (the 250s are not recommended for this), but your listening levels are going to be limited (how many dB you get out of them). Beyerdynamic created a set of low-impedance for a reason - and if your laptop / phone / or PC with no external amp/dac or amp'd internal card are your primary use...then you have your answer.

Headphone Folding Features	Over Ear
Headphones Ear Placement	Over Ear
Style Name	Headphones
Color	Gray
Connectivity Technology	Wired
Headphone Jack	3.5 mm Jack
Audio Driver Type	Dynamic Driver
Impedance	250 Ohm
Noise Control	Sound Isolation
Unit Count	1.0 Count
Item Weight	10.24 ounces
Is Electric	No
Antenna Location	Recording
Compatible Devices	Studios
Additional Features	Innovative bass reflex system, High wearing comfort thanks to soft, circumaural and replaceable ear pads, Circumaural headphones for professional sound in the studio and on mobile devices, Comfortable fit due to rugged, adjustable, soft padded headband construction, Made in Germany
Enclosure Material	Steel
Specific Uses For Product	Studio

beyerdynamic DT 770 PRO 250 Ohm Over-Ear Headphones in Gray. Enclosed Design, Use Ideal for Studio Mixing

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