I will break the comparison into three parts looking at bass, mids and highs and tested them with an iPod classic and through a benchmark dac 1
Bass - both have great bass, the srh 840 has a little more mid bass bloat which gives the impression that you have a bass boost on. The dt250 is tighter and cleaner
Mids - both are nice and smooth with the dt 250 sounding a little cleaner due to the lack of mid bass bloat from the srh840 although the srh 840 is a little warmer due to this.
Highs - both have nice treble, the dt250 is smooth and non fatiguing. The srh840 is not not fatiguing either but is a little brighter and shows off a touch of sibilance on hot recordings.
I was in love with the srh840 when I first heard it and would have been happy to stay with it if I hadn't put it head to head with the dt250 but as this addiction grows in you. Yu just have to try the next best thing and I am glad I did because I find the dt 250 to be more to my liking thus I have returned the srh840. A much cleaner and more accurate representation of the music. As others have said they just get out of the way of the music and let it flow through.
Both are great all rounders that sound great out of the iPod and scale up with better amplification.
As I said if I had never heard the dt250 I would say that the srh840 was the best closed cans around - but now I say it comes in a close second.