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.

Noise Control	None
Headphones Jack	3.5 mm Jack
Model Name	DT 770
Connectivity Technology	Wired
Included Components	1/4" Gold Plated Adapter, Beyerdynamic DT 770 PRO - 80 Ohm Black, Drawsting Carry Bag
Age Range (Description)	Adult
Material	Plastic
Specific Uses For Product	Professional
Compatible Devices	Universal
Cable Feature	Tangle Free
Item Weight	12.2 Ounces
Customer Package Type	Standard Packaging
Net Quantity	1.0 Count
Style	Headphones
Control Method	Touch
Number of Items	1
Product Dimensions	25.4 x 20.32 x 12.7 cm; 345.86 g
Item model number	717770
Connector	connector type
Hardware Interface	3.5mm Audio
Size	80 OHM
Item Weight	345 g
Manufacturer	beyerdynamic

beyerdynamic DT 770 Pro 80 ohm Limited Edition Professional Studio Headphones, Black

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