I think before everybody jumps the gun here, the biggest question is which headphones from within the two lines are you looking at?
I'm guessing you're looking at each Brand's entry level headphone, which would be the SR60i and the D1001. I happen to own both of those headphones, so I'll point out the differences.
The most easily noticeable difference is the amount of bass. The D1001 has a LOT of bass for a low impedence headphone. Some call it bloated and out of control, and while I think that may be the case, its not like its BOSE bass that just runs all over everything either. It's quite punchy bass. It lends itself to a much fuller sound that Grados have. This full sound is what I think some people mean when they say its bloated, but in my opinion the full bass doesn't "get in the way" of the midrange, it provides a strong foundation for the midrange and hi frequencies to sit upon.
The next most easily noted aspect is that the Grados are a lot more "upfront" than the Denons. The Denons are a pretty "upfront" headphone, but Grados are probably the most upfront headphone of any major brand. With Grados you feel like you are sitting on the stage. Some people like this, some people say it destroys soundstage nuance. This isn't to say that D1001's have a better soundstage. They don't. Neither headphone has much soundstage to speak of. Things sound like they are either coming from the right, the left or some point in your head in between.
Both headphones have an upper mids peak. That is, with both headphones there is a discernable emphasis on the upper ranges of the normal vocal range. These are the so-called "presence" frequencies. This is why both headphones sound so upfront. The Grados emphasis sits squarely on the presence frequencies, while denons are a little bit higher up with their emphasis (they actually lie in teh presence frequencies of the violin, which is why violins tend to just jump out of your headphone on D1001s).
Grados have a lot quicker drivers than the Denons. This means that really fast passages retain their definition much more easily than with the Denons, which tend to turn into mush with really fast guitar passages. This also has to do with the Grados being completely open and having virtually no reverberation issues. While the Denons seem to have non-major, but discernable issues with cup reverberation.
While I think Grado discomfort is way overhyped, D1001s are certainly significantly more comfortable. The Grados will likely have to be stretched out some so that they are just tight enough that they stay on your head, but no tighter. This helps with comfort, but also helps with sound, as it puts the drivers in the position relative to your ears where they are supposed to be. Denons are also signficantly more portable, due to the fact that they are smaller, clamp on your head without being uncomfortable, have a shorter cord and dont get twist issues like Grados do (since grado cups can swivel around freely when not on your head). You also don't have to worry about things getting into the back of the driver with Denons, since they are closed. With grados you have to be careful that dirt, hair, water, etc aren't going in through the back and messing up the driver.
In summation there are just a couple of main concerns and differences between these headphones:
1) if you are a "basshead" just get the Denons.
2) If you are all about hearing detail in blistering guitar solos or really like to feel like you are sitting on the stage with the band, get the Grados
3) If these will be mostly for on the go, get the Denons
4) If you can't deal with even the smallest amount of discomfort, get the denons.
5) Hip-hop and R&B should probably favor the D1001
6) Classic rock and metal should probably favor Grados.
That's all I have, and again, this doesn't apply if you are looking at SR225's v. D2000's or RS-1's V. D7000's
