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.

Sensitivity	96 dB
Headphones Jack	3.5 mm Jack
Model Name	DT 770 PRO 250
Connectivity Technology	Wired
Wireless Communication Technology	Wireless
Included Components	Headphones, Jack Adapter 6.35mm, Protective Case
Age Range (Description)	Adult
Material	Plastic
Specific Uses For Product	studio
Recommended Uses For Product	Recording
Compatible Devices	studio
Control Type	Noise Cancelling
Cable Feature	Retractable
Item Weight	0.38 Kilograms
Water Resistance Level	Not Water Resistant
Customer Package Type	Standard Packaging
Unit Count	1 Count
Style	250Ω DT 770 PRO 250
Control Method	Remote
Number of Items	1
Audio Sensitivity	96 Decibels
Batteries Required	No
Frequency Response Curve	5Hz-35000Hz
Item Shape	headphone headband
Manufacturer	beyerdynamic
Item Model Number	beyerdynamic
Size	250 OHM
Model Year	2000
Product Dimensions	17.78 x 10.16 x 21.59 cm; 380 g

beyerdynamic 密閉型オーバーヘッドヘッドホン レコーディングモニター用 DT 770 PRO 250

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beyerdynamic 密閉型オーバーヘッドヘッドホンレコーディングモニター用 DT 770 PRO 250