Well, to defend DPA a bit. I´m very much a fan of them.
DPA4006 started life inside Bruel & Kjaer, a well respected firm doing measurement equipment. Especially known for their measurement mics. According to the official story, which I believe to be mostly true, a devoted engineer tried to adapt their measurement mics to beeing used as recording mics. The problem they had to solve was the horrible phase response which you typically have in measurement mics. The 4006 took a lot of development in order to keep all the good things from the measurement mics, and remove all the things you do not want in a recording mic. (Phase response is not a problem in measurement mics, what you aim for is a very straight frequency response).
You can find older mics marked with B&K4006, this is the same mic as DPA was spun off from B&K a few years ago.
The 4007 has a smaller diameter mic capsule and a lower sensitivity. This is made by purpose to allow you to record stronger sources without distortion, and now we are talking things like inside a bass drum, an inch from the skin, or racing engines and things like that.
The 4006 is one of the rare class of established standard mics in classical recording, symfony orchestras and such. One of its few problems, or strenghts if you like, is that it has an output transformer. The 4003 solves this by not having a transformer, and additionally feeds the head amp in the mic with 130V DC to get some extra mileage out of the mic.
I own a pair of 4003 and a pair of 4007. For most usages they create very much the same sound, they are both really good omnis. The 4003 has the edge in going lower in frequencys and is THE standard for organ recordings. It also has the edge in lower self noise.
I have not actually used the compact versions of these mics, but I would expect them to sound very similar. You would probably be hard pressed to make out any difference. The smaller mic though has a bit higher self noise. There is one more difference as to the available accessoares. On the larger mic you can exchange the grid to change the acoustic sound a bit. There are currently three grids avaiable. You can also use the acoustic modifiers, balls, on that mic. On the smaller mic the grid is fixed and you cannot use any acoustic modifiers. This may be an important issue to you or not.
All-in-all, it is difficult to go wrong with either of the DPA-s.
You might however want to look into the even smaller, you migh say tiny, 4061. Despite what it looks like and how it is sold, this is really a good general purpose omni mic. (You will need a microdot to XLR adapter). The small size is traded in with yet a bit more self noise. It depends on what you are planning to record if this makes any difference.
Gunnar