In this TEDx Talk, KEBU discloses some points why he prefers analog synths for his music. He mentions three major reasons which I’d like to second:

• Sound: Compared to digital synthesis, each note (and even voice) on analog machines sounds slightly different, and the sound also changes depending on further parameters, like the temperature or age of an instrument. Some digital synths try to emulate this, e.g. by slightly detuning the oscillators over time or notes at each keypress. But I’ve barely heard convincing results so far. Thus I really like his example comparing digital and analog drum machine sounds.
• Feel: He mentiones the unreliability and latency of software. Yes, it is phantastic what one can do nowadays with digital studio software (and I doubt there are many people who wanted to dismiss software completely). On the other hand, physical devices provide dedicated hardware controls. I meanwhile even prefer devices with keybeds of their own over rack mounted or desktop synths.
  One further issue is latency. I exclusively played digital synths during the 90ties. When I first touched an analog machine (the Roland SH-101), it felt completely different. There was an immediate response on each keypress. It’s quite interesting how a couple of milliseconds of latency impact ones playing.
• Limitations: Removing options removes distraction, leading to focus and more creativity.