This is going to be a bit of an odd comparison of the Beyerdynamic dt880 ($225-250) and the Grado SR60 ($69, haha), but here it goes. For a "compact statement" see the summary at the end.
The first thing I notice between the two is a severe lack of soundstage in the sr60's, and i think this tends to represent the Grado house sound for the lower models.
Second thing is that the highs don't seem to extend as high as the dt880s. Despite this, they seem a be ample in quantity to not sound veiled, and the lower-highs have plenty of detail (cymbals are pretty well detailed as well as other instruments in the 6-12kHz range). I don't find the sr60's harsh in any way at all compared to the dt880, but i love hearing those highs, so they're both right up my alley.
The mids to me seem to be comparable in regards to distorted guitar reproduction. Lower mids seem to be punchier on the sr60--drum kicks and fingering of basslines is a tad more apparent; I would attribute this to the Grado sound. There's a slightly different coloration of the mids by each, but this difference isn't night and day to me. Both are very clear, letting guitars come right through, though due to lack of soundstage on the SR60 the guitars tend to be in your face, while there is a bit more of a spatial awareness gained by the dt880. I noticed the OP said somewhere that he didn't like the distance between him and the music, and this lack of said distance is another attribute of the Grado sound.
Bass is very detailed and accurate on the dt880s, not accentuated beyond whatever is captured in the recording. The bass is slightly louder on the sr60's, and nearly as accurate in detail, though not in quantity if the dt880 is your preferred reference in bass (and it is for me, I think it does bass perfect).
So in summation: The dt880 is all about soundstage, great highs, great mids, accurate, non-accentuated bass (some might call this lean or quiet), and fantastic comfort. The SR60 has good highs, great mids, fairly good bass with regard to quality that is quite punchy and might be considered 'fun', but no soundstage and comfort is questionable for some (though I have no problem with them).
I wouldn't extrapolate any of my observations to cover the sound produced by the dt770 or dt990 given that each is known for very different things (770->bass, 990->U-shapedCurve). I'm not sure if a beyer "house sound" even exists, as it varies so much from model to model. However, I believe there are certain universal attributes apparent in most Grados, which I noted above (punchy midbass, those "grado mids(tm)")--this is the sole reason why I even bothered to write this mini-comparison.