EDIT: After reading my own post, it was apparent that I've had a long day, am very tired, and can't write worth a crap now. Sorry about that.
Just returned from East Hamilton Radio (big audio retailer), after having A/B'ed the SRH840, and the SRH440. The source was CD audio (electronica) and both headphones were driven from the same Denon reciever, out through a distribution headphone amplifer (not sure which model). Here are the obvious observations to my ears:
Bass
SRH840 had greater bass quantity, definitely on the greater side of neutral. The bass extension was great, and was still well controlled, but seemed to seep into the midrange, making everything very warm sounding. SRH440 had tighter bass, which is likely more neutral, and similar to the quantity of my DT880 ('05). The extension was still good, but there was no sense of warmness at all.
Midrange
Simply put, the SRH840 midrange was soft and warm, and the SRH440 midrange seemed thinner, but was still a standout amongst the whole frequency response. I've noticed that string instruments and piano really seem to stand out on the SRH440.
Treble
This was very obvious. The treble on the SRH840 was rolled off relative to the other frequencies (but not in a terrible way). It offered a much more laid back listen, and switching over to the aggressive treble of the SRH440 was like night and day. While neither was "better or worse", there was no mistaking that the SRH840 was more akin to Sennheiser, and the SRH440 was more akin to Grado as far as treble was concerned. Still, no sibilance in either phone.
Soundstage
The soundstage on the SRH840 was certainly bigger, and as a result, instrument separation seemed better. This also seemed to coincide with the laid-back presentation of the SRH840, again similar to the Senns. The soundstage on the SRH440 IMO is still better than other closed cans that I've tried such as the V6 and K240, but noticeably more forward than the SRH840.
Detail
While the SRH440 has clearer treble that gave you that more "in your face" detail sound, I think the SRH840's better instrument separation and soundstage may ultimately offer a slightly more analytical listening experience.
Of course, none of this is definitive. There is only so much you can glean from a short period of listening in a retail store, but to these ears, the differences were fairly noticeable. I would still suggest that the SRH840 is a warmer-toned, laid back sophisticated phone, whereas the SRH440 is a more neutral, forward and energetic listen.