I have owned both for a few months now. They are both excellent sounding, but are polar opposites in terms of sound signature. MSR7 is quite forward sounding with a fast, snappy attack, emphasis on the upper mids and lower treble with a slight lack of bass relative to the mids and highs. SRH1540 has a warm tilt to its sound with emphasis on bass, particularly the sub bass below 100 Hz. The upper mids are much more withdrawn on the Shures relative to the MSR7 and the sound of the SRH1540 is quite a bit more spacious (or distant, depending on how you look at it) and more laid back.
In terms of pure sound quality, MSR7 edges out the SRH1540 in bass tightness and definition, as the former has significantly less distortion below 200 Hz, especially at high volume levels. However, I cannot say that MSR7 has better bass - I think SRH1540 actually has the more satisfying low end. Despite having cleaner bass, MSR7 can also lack punch and presence down there, which SRH1540 has in spades. Actually, SRH1540 can have the opposite issue of producing somewhat excessive amounts of sub bass with some music, especially at high volumes. Overall, I think SRH1540 has a more natural bass presence and I can actually hear more low level information, more texture in the bass of the Shures vs. the MSR7, even though the bass on the Shures is a tad looser, less controlled.
Mids can sound overly forward and shouty on the MSR7 with some music, especially lively, energetic recordings. In terms of sound quality in the mids, I think SRH1540 actually beats the MSR7. The Shures have stellar mids. The midrange on the SRH1540 is extremely resolving, especially in terms of micro detail retrieval/texture, but also has a very pleasing, warm tone to it - just a bit of coloration - that adds magic to the sound. I guess one could say that SRH1540 has those classic Shure mids. Just yummy.
Male vocals are probably the best I've heard on the SRH1540. The only issue with the mids on the Shures is that they are a tad recessed relative to the bass and highs, so they can sometimes lack a little bit of presence. MSR7 doesn't sound quite as textured in the mids as SRH1540, but does have more perceived clarity, probably because the mids on the MSR7 are much more forward vs. SRH1540.
The lower and mid treble is more edgy and forward on the MSR7. The highs on the MSR7 are extremely resolving and clear, but also have a hint of some unnatural metallic coloration at times - just a hint though. SRH1540 has very natural highs - I think more natural than those of MSR7. The Shures have a softer, more polite treble, but with very little loss of perceived clarity and similar, if not quite the same level of treble resolution that MSR7 has. Like with the mids, the highs on MSR7 are simply easier to hear because they are more forward sounding. SRH1540 doesn't draw attention to its highs, but the quality is still all there on the Shures. I would say that both have extremely good highs for closed back dynamic headphones and actually approach the very best open headphones in treble quality.
Soundstage is rather small and shallow on the MSR7, although imaging is very sharp and well defined. I would say MSR7 has a decent soundstage for a closed back headphone. SRH1540 does much better and actually has a pretty darn spacious sound for a closed back, approaching the spaciousness of my HD600 and K612 Pro. Soundstage width is not really great on the SRH1540, just OK, but soundstage depth/layering is remarkable. SRH1540 can, at times, convey more perceived depth to the sound than even my HD600 and K612 Pro.
SRH1540 seems to have wider dynamic range than MSR7 - the Shures can convey dynamic contrasts in music more effectively, more vividly to my ears. The remarkable soundstage depth/layering of the SRH1540 certainly helps with this also, while MSR7's lackluster layering makes it sound less dynamic than it probably is.
Both are easy to drive with MSR7 being a tad more sensitive and louder than SRH1540 at the same volume setting. For whatever reason, despite being extremely resolving and clear, I don't feel that MSR7 scales nearly as well as SRH1540 does with better amps and DACs... Even though MSR7 seems highly resolving, I think that this is at least partially the result of its forward, aggressive presentation. SRH1540 is far more distant and laid back and so it may not seem as resolving on brief listen. However, I think that careful listening reveals SRH1540 to be perhaps even clearer and more resolving. At least, the mids definitely sound more textured and articulate on the Shures vs. MSR7 to my ears...
Those who like their music fast, forward and exciting may prefer MSR7 sound greatly. Those who like a smoother, a more relaxed approach may greatly prefer SRH1540. Personally, I think SRH1540 a has higher sound quality overall, but doesn't impress as much as MSR7 on first listen. MSR7 is a great headphone to bring to headphone meets to impress people. lol
Also, keep in mind that neither of these two headphones is a great option for those seeking a neutral tonal balance, as both deviate from neutrality by a good margin. MSR7 is too forward in the upper mids, while SRH1540 is too emphasized in the sub bass... For a more even tonal balance, I would look into NAD Viso HP50 and Focal Spirit Classic and Professional. Oppo PM-3 also seems like a good option for a neutral tonality.