In my opinion, there's a little bit of truth to all of the above. But, when the vintage synth market really took off in the late 80's and early 90's, the current synths at the time were pretty lame. Most of the synths in the studio at the college I go to are from this period, and I hate them all. For my projects, I usually used the samplers and softsynths. In another thread recently, the issue of synths from this dark age in electronic music not having resonant filters came up, and Nigel told us how at the time you simply couldn't make a digital resonant filter, and an analog one would be too expensive. Given the alternatives during this time, I could see why the popularity of vintage synths exploded.
In another studio on campus, we have an all analog room with all kinds of stuff, like a Korg MS20 and that quirky thing with the joystick and battleship-style pegs. I didn't really get into those, but the one synth with the sound that I absolutely adored was an old Arp 2500, a big as box full of various moduals. That is the only analog synth I'd actually splurge for if I had the money.