Boojum,
this is sort of a difficult question to answer. You have to help out in telling us your intended use.
Both are at the very top professional quality layer of small diameter condenser omni mics. Both are very often used in classical recordings (think, mics on a symphony orchestra) . The main cost of a classical recording is paying maybe 50 musicians, so the cost of the microphone is not an issue there. Less often used in the pop studio arena. The difference between them can be argued but is mostly on the "matter of taste" scale. You will not go wrong with any of them, unless what you need is a different type of microphone (maybe a cardioid) .
The Schoeps are old work-horses in the classical arena and is a two part mic, body + capsule. The MK2h has a small high frequency rise to compensate for the loss of high frequencys experienced at a medium distance from an orchestra (or similar). The Schoeps range has quite a few other capsules to choose from, simply looking at the omnis there are the mk2 and mk2s nicely bracketing the mk2h in amount of high frequency rise. The CMC6 is pretty much the normal choice of body, although they have some choices there as well.
The DPA-s are old work-horses in classical as well. They started out branded B&K, in fact the actual capsule is still marked with that brand (long story) . The same capsule can be found in the 4003, the 4006 and the newest 4006TL. Personally I run the 4003 and has always been happy. These mics comes with exchangeable grids, allowing tailoring the high frequency rise to get similar results as with the three Schoeps mentioned above. I would be happy with either of the mics, with a slight preference to the 4003 and probably putting the 4006TL next on the list. But the 4003 needs a special power supply increasing the system complexity. There is even a service available where the manufacturer modifies your 4006 to become a 4006TL at a fee if you preferr the difference in sound.
Both manufacturers has been around quite a while and both can service your mics if the need arises.
In the same kind of arena you find mics like some of the Neumann mics, the Sennheiser MKH-s, and a few other brands. Which sort of concludes the discussion, it is about small differences down to your taste. A "real" engineer migh have both available depending on the situation. Only way to choose in my mind is to actually test the mics in your real life recordings.
Gunnar