Hi, I've owned or still own all of the headphones you mentioned. Generally speaking, I'd say that they are all excellent headphones except for the PRO900.
Here are some details:
DT880
This is a fantastic semi-open headphone with a neutral sound signature that is not really flawed in any significant way. Even though they are neutral and have fantastic bass and great mids, they also do have a Beyer-style treble emphasis that gives them very sparkly and impressive treble, a real treat for treble lovers but perhaps overkill for people overly sensitive to sibilance. Their mids are a little recessed but not in a significant way; however, due to their very slight V-curve frequency response, these headphones generally work best when played at low volumes. They are very comfortable and have a fantastic soundstage and they are also built very well, certainly made for years and years of use. There are many versions of this headphone and even the 32 Ohm version benefits from an amp, while an amp is basically required for the 250 and 600 Ohm versions to sound as they should. These headphones come with a soft case but do not fold in any way, making transporting them less practical than the other headphones here. Being semi-open, they can really only be used in a quiet environment, while the other headphones here are closed and seal rather well, allowing for fairly comfortable outside use.
PRO900
The bass on these is very powerful, impactful and of quite high quality; however, sadly, this is the only good thing I have to say about these. Well, OK - they come with a nice and practical hard case, they have removable cables and they are quite comfortable. They also look rather nice and when holding them in your hands, you can easily feel the amazing quality of all the materials used to make them. They fold completely flat and also can be folded into a ball for transportation, making them by far the most practical in that regard. They also have a nice soundstage for a closed headphone due to the S-Logic technology that they use, however, this soundstage does sound a bit artificial. Sadly, once you actually start listening to them, it becomes obvious that besides the bass, everything else is painfully harsh and piercing, with a shrill, metallic characteristic to the sound. Female vocals with these headphones sound like something is being drilled into your skull and the treble is immensely prone to sibilance. They have a very uneven frequency response curve and certainly cannot be called neutral. I wish these headphones sounded better
AKG K550
Neutral sound with very high quality, clear and impactful bass. I'd say they have some of the best bass around, as long as you are not a total basshead. The mids are similarly awesome with voices being rendered very naturally and without any annoying sibilance. The treble is also very clear but not emphasized, which gives these a very non-fatiguing sound.... for most. Those who are particularly sensitive to driver ringing often have a problem with upper mids on these headphones as they can sound a little harsh due to their clarity-focused sound signature; however, it should be stated that the level of harshness here is lower than with the Ultrasones or with Grado headphones, for example. The harshness can also be mitigated somewhat by modifying them (by removing the rubber 'condom' attached to the back of the drivers and damping the enclosures with some cotton), as well as by using a warm amp. They do not actually need an amp to sound good though and can be driven without any issues out of most sources, as long as they have low output impedance. These also have a very premium build quality, elegant looks and are supremely comfortable. They have possibly the best and most natural sounding soundstage of any closed headphone, certainly better than the PRO900, which sounds artificial, and the SRH940, which actually has a very nice soundstage but not as spacious as the K550. People with small heads often have problems achieving a good fit with these, which compromises their sound. For me, they are the best truly closed circumaural headphone around, at least below the flagship level. Their cable is very long and not removable; however, luckily the cable is of very high quality and can be braided easily or simply folded into a ball as the cable is very tangle-free. They do fold (nearly) flat for practical transportation but do not come with any sort of case, which is a very big shame. It is a good idea to invest in a third-party headphone case with these.
SRH940
Very clear sound with lots and lots of detail retrieval. Even with this big emphasis on clarity, treble and upper mids, they do not sound fatiguing and also have a relatively spacious sound for a closed headphone. They are easy to drive and sound great even out of an integrated source. They fold nearly flat and also fold into a ball; however when folded, they are not as small as the PRO900. They come with two removable cables (one coiled, one straight) and come with a very nice hard case which is very practical. They do benefit from an amp that has a bass boost though since they are bass-shy headphones with a noticeable mid-bass slump. With the bass EQed up a little bit, I'd say they have a superb, neutral sound that is very clear. I would not advise getting these without first trying them out since they can be very uncomfortable for many people, due to their headband design. I sold my SRH940 for this very reason - loved the sound but simply couldn't wear them for longer than 30 minutes...
In terms of sound quality only, this is how I'd rate these headphones:
DT880 > K550 > SRH940 >>>>>>>>> PRO900
