I’m a total noob to audio technology and verbiage. I listen to a lot of classical, jazz, choral, some alternative and vocals like Sinatra etc.
Hey no worries bud, from my experience with the two I'll try to help you out as much as I can.
Build/ Comfort:
The Mh-40's and PM-3's are both built well and with good materials (metal, quality construction). The MH-40's are a little smaller which is an advantage for portability, but are not as comfortable as the PM-3's in my opinion. The cups on the 40's tend to swivel freely, where the PM-3's have a more robust swivel mechanism. The headband on the PM-3's are more comfortable and padded. Both have nice earpads, but the MH-40's are more narrow. If you have bigger ears you may find them distracting.
Isolation:
The PM-3's isolate sound better than my alcantara MH-40s. This is because the alcantara material leaks more sound than protein leather. Both would still be good for commuting, but the PM-3's would edge the 40's out in this area.
Portability/ Accessories:
Both are easily portable as they are light and easy to carry. The MH-40's come with a fabric carrying back with a magnetic strip to close the top, and the PM-3's come in a Denim carrying pouch. The denim pouch is more protective.
Both come with two cables or various length where one cable has smartphone controls and microphone. The MH-40's are fabric covered cables where the PM-3's are rubberized. I find the 40's cables a lot easier to manage and put away.
Sound:
Now take this as you will because my impressions are subjective. However, I hope I can explain my findings in a way that helps you in your decision.
MH-40's:
The 40's are a closed back dynamic driver design with quite fun sound signature. The bass/ mid-bass is elevated and the highs are rolled off. The bass/ mid bass will sound warm and full, and drums will have a good punchy thump. I find the bass to be a bit bloated and lacks clarity, but it makes up for it in feeling. Using jazz as an example, bass guitar, double bass and jazz guitars will have a nice full sound. The bottom end of a sax or trumpet will also have a good weight, like you can feel the reverberation off the brass. hats and symbols will sound like they are quieter in the mix since they are rolled off. So they are not fatiguing or bright. I do find unevenness in how the sound of the highs are rendered. Meaning, it just doesnt sound smooth all the time.
The biggest pro of the 40's are how dynamic and full of energy they are. You can feel that the sound has a lot of character, has a thick sound, and its fun to listen to.
The biggest problem with the 40's are that instruments sound compressed and lack detail. What I mean is that for jazz or classical, it will sound like instruments are all being played between the width of your ears, from one to another, and the sound is narrow. It gets a little muddy and can be unenjoyable to try and pick out how an instrument's natural decay or timbre sound.
PM-3's:
The PM-3's are a planar magnetic driver headphone that have a neutral, more flat sound signature. Where the 40's have a thicker, more weighted/ unbalanced sound, the PM-3's are much more refined, controlled and balanced. Planar driver headphones typically are better are reproducing accuracy of instruments and have a tighter, more accurate bass response.
Like the 40's the PM-3's have a laid back and rolled off treble. This makes an easy to listen to experience without fatigue. Unlike the 40's the PM-3's are more detailed, have better imaging, and no bloat. The bass is tight and articulate, but not as bassy or mid bassy as the MH-40's. They will deliver a more accurate representation of the song. Sometimes you may find them bass shy if you like hearing a more full sound. Bass doesn't bleed into the midrange, and instruments sound nice and detailed. Where the MH-40's instrument representation sounds compressed, the PM-3's will do a much better job of letting you hear the placement on an instrument, its characteristics, without being muddy.
The biggest pro of the PM-3's is its neutral/ natural presentation with a tighter bass, smooth, more detailed sound.
The biggest problem with the PM-3's are its small soundstage (think ear to ear), but since the presentation is flatter/ less dynamic, it sounds a little more narrow than the MH-40s
A thing to note about the PM-3's are that, due to being more neutral or flat, some people will find them boring sounding since they don't have the same energetic or dynamic sound of the MH-40's or other dynamic driver headphones. Its really a difference between more fun sounding (MH-40) versus a more articulate sound (PM-3's). For Jazz and classical, I feel like the PM-3's will have a much better midrange and instrument separation.
Another thing to note, the MH-40's will be more easily driven from the headphone out of a smartphone than the PM-3's. Planar magnetic headphones, and what I've heard about the PM-3's, is that they preform better with a more amplification, such as a portable dac/amp or amp.
I'm sorry for this wall of text, but I hope this is helpful to some degree. It would be best to consider which one would be easier to try and return if you didn't like it.