The sound differences between the various impedances are very slight and most people can only actually hear them when the sounds are compared directly. They are, in any case, smaller than the differences between any one of these variants and competitor products.
In general, it can be stated that the resolution and precision of the high mids and highs is slightly better at higher impedances. There are barely any differences worth mentioning apart from this.
The variants of DT 880 Edition and DT 990 Edition with higher impedances (250 ohm and 600 ohm) should only be used by people who
- already own such a model and want to replace it,
- insist on the (minimally) better mid- and high-frequency playback,
- are sure that the headphones will at least not be used on mobile players,
- can, particularly for operation of the 600 ohm version, provide sufficient output voltage on the device to which the headphones are connected.
To reiterate clearly:
The low-resistance, 32-ohm headphones are also an absolutely high-quality variant with excellent transmission characteristics that match the best competitors in the price class. If you want a flexible and sufficiently loud solution, you are better off using the 32 ohm version in most cases. All sound advantages of the 250 ohm and 600 ohm variants are ultimately of no benefit if the headphones on the player being used do not produce the required volume.