I have both (QB2 and MH1C). In the general sense, the QB2 is slightly V shaped with treble emphasis and the MH1C is a slight V shape with more bass emphasis.
Head to head in each category:
Comfort and build: Both have very good build quality (MH1C is slighlty better). The narrow flat Y cable on the QB2 is excellent, average microphonics. The flat J cable on the MH1C will make you want to hang yourself with it. The QB2 has a flatter and wider houding with the nozzle at an angle, MH1C has a slim longer barrel. Fit is subjective. Accessories are equally sparse.
Bass:
MH1C has oodles more sub-bass. Midbass quantity is also at a similar level. Fo the quantity it is chucking out the quality is quite good (but not to my taste). Vent mods will tighten the bass and make it feel more controlled.
QB2 has a midbass hump which is still lesser than the MH1C and sometimes(depending on the genre) does not fit well with the otherwise superb response. Sub-bass quantity is much lower than the MH1C but extends and shows up when called upon. Whether the sub bass quantity is sufficient or not will depend on your preference. Midbass quantity is definitely sufficient for most genres, though it lacks a little control.
Mids:
Notes carry nice weight and warmth on the MH1C and is more lush. Both are fairly accurate. Mid-bass spills a bit into the lower mids. The mids are very good but cannot hope to shine/be-prominent because of that bass. The QB2 is also slightly recessed in the mids(mid-bass slightly interferes), more so because of the prominent treble.
Treble:
MH1C is smooth, forgiving and natural. Is edgy at times but not bothersome.
QB2 is a clarity oriented phone and sports prominent treble. But, it "never" gets sibilant especially when you expect it to. Even with that 8k peak.
TL;DR: Both are emphasized on opposite ends of the spectrum. MH1C is bass heavy in comparison. QB2 is relatively more neutral with prominent treble but the midbass lift does inject some punch and warmth. The cable is beyond terrible on the MH1C. Treble is very good on both albeit for different reasons.
If neutral and analytical is your aim, the QB2 comes closer (after a midbass EQ cut)
If warm and natural is your aim, the MH1C will come closer (after vent mods)
Personal biased opinion: I love both but the QB2 slightly edges out the MH1C for me.
The cable and heavy bass (even after the mod) were the cons with the MH1C. The occasional midbass eccentricity and slightly recessed mids are cons.on the QB2.
THis is of course a broad description. If you want to know anything specific, let me know.