I found no difference between an iFi power supply and an apple iPad power supply when I used them with my D50. Both are switching power supplies in that they use a power transistor to create a high frequency voltage which is then stepped down to produce the DC voltage required (e.g. 5V) and then that is smoothed out. It's this smoothing (and the accuracy of the high frequency voltage) that is done better in the commercial switching power supplies. Relative to an LPS, they are quite compact and efficient (and cheap).
A linear power supply is a big ugly box that supplies a nice, clean DC output voltage, but it operates very inefficiently, so it generates a large amount of wasted heat. LPS's are usually 'cleaner' than switching power supplies for their DC outputs, so may have a positive impact on the sound from audio equipment. They usually cost a lot more than switching power supplies.
Here's an old picture of my headphones system were you can see an LPS next to my D50.
i also use amiron with d50s