I owned both and I also owned several other closed cans around that price range. IMO HD25-1 and M50 are on about the same level overall. Both have strengths, but also some fairly serious flaws. HD25-1 has excellent detail resolution and a pretty balanced overall sound that works well for a lot of different music. However, it lacks smoothness, especially in the treble and bass definition and depth with the stock cable isn't all that great, even when it is amped. Don't get me wrong, HD25 has very good quality bass for a closed headphone of its size, but there are just better sounding closed headphones out there available at the same, or lower price. ATH-M50 delivers a much smoother sound than HD25, with a more even tonal balance in the mids and highs, but gives up quite a bit of micro detail compared to HD25, especially in the midrange. The detail resolution of M50 should be adequate for non critical listening though, such as general portable use in moderately loud environments, such as walking along a moderately busy street or riding a fairly quiet bus/train, where you won't be able to hear subtle details in your music anyway. In very loud places, such as the subway, over the ear closed headphones do not provide adequate isolation, not even the HD25 - you will want IEMs for that. M50 also has a better soundstage than HD25 - it is wider, deeper and with more realistic instrument placement/imaging, especially when they are amped and I think M50 really benefits from an amp a lot - more so than HD25. Unamped, the bass on M50 is generally not very good IMO - it is quite boomy and muddy compared to many other headphones in that price range or even cheaper ones. Well, that is unless you are using a very good DAP and I think a Teclast T51 should be good enough to drive M50 fairy well. When amped or driven by a good portable DAP., the low end on M50 tightens up significantly and becomes quite nice actually - very deep and punchy with decent detail. But still, even when amped, I think M50 can sound a bit unbalanced in the low end, with the lows intruding into the lower mids sometimes. Generally, I didn't not find this to be a serious issue though. I do think HD25 has better quality bass overall, but M50 does go deeper and provides a more satisfying impact for bass oriented genres, such as trance and electronic, so it may suit you better.
In that price range, there is also another nice, bassy can suitable for trance and electronic and that is the Shure SRH750 DJ. It's usually around $150 new, but you can find one for less than that. It is somewhere in between HD25-1 and M50 in portability - smaller than M50, but larger than HD25. Isolation is more similar to M50 - less than on HD25, but still decent. Build quality seems decent, but not as good as on HD25s, which are built like tanks. The SRH750 DJ sounds like a more refined ATH-M50 to my ears overall with a bit more bass and a slightly recessed midrange. Detail resolution is better on SRH750 than M50 and bass is more controlled, especially out of weak sources, like the Clip. With some music, SRH750 can get a bit too bright in the highs, but the treble is of better quality than on ATH-M50, with the former sounding more textured and organic and the latter more metallic and synthetic. Soundstage size is about similar between the two, but the Shures sound more open IMO, whereas M50 is more cupped in by comparison. Compared to HD25, SRH750 has a much larger, more airy soundstage. HD25 is more neutral in the bass and treble and more refined, but SRH750 is more neutral in the mids, smoother and more powerful sounding in the lows.
So in a nutshell:
M50: Smooth; laid back; dynamic; fairly neutral; scales really well with amping; well extended, but somewhat unnatural (metallic) highs; spacious, but somewhat cupped in soundstage; deep, punchy bass that needs some juice to tighten up, but regardless of source can sometimes get out of control and creep into the mids - doesn't happen often though; mediocre micro detail retrieval, but good separation; works best with bass oriented electronic music; not the best for vocals and real instruments; long burn in period ( at least 100 hours)
HD25-1: Excellent micro detail; great reproduction of vocals; good dynamics, a fairly neutral frequency response; bass is fairly tight, but lacks some definition and depth; highs are a bit peaky and slightly grainy, but well extended; doesn't scale as well with amp as M50, but amping it is still preferable; soundstage is small and closed in, but imaging is very nice and sharp; a good all arounder - works well with most music
SRH750 DJ: The best bass quality and extension of the three; Great treble extension; very even mids, but recessed compared to bass and treble; dynamic; very decent detail and great separation, but lacks some refinement compared to M50 and HD25; the most natural treble of the three, but a bit grainy and peaky compared to better headphones; a very good soundstage in openness, size and imaging; best suited for bass oriented music, but works well for most other genres too if one can tolerate the V-shaped frequency response or has good EQ on his source; doesn't need amping at all to sound great
