What can an analog sequencer do that MIDI can’t? I am (too) familiar with MIDI and I can create looping sequences with notes and control changes. Yes, miracle technology. But what inspirational things could an analog step sequencer do which MIDI and all those menus and screens might not achieve? I need cold hard facts so my cold hard cash can feel a little less guilty 
Tweak what you want, in realtime, without diving into a convoluted menu system.
Just been looking up the Doepfer MAQ and now realize that you can have analog steps and midi too. Playing random and pendulum seems like a lot of fun too.
Live control over the sequence. The Q-960 Moog and the STG Soundlabs time suites are the most ‘playable’ conventional analog sequencers out there. Then there are some other machines that are remarkable, yet digitally controlled. (MAQ 16/3, GenoQ Octopus, FR Orb, etc) All of them are more immediate than any MIDI sequencer and allow freeform improvisation.
This is an example of the STG suite in operation. It really begins to get interesting at around 4 minutes but the begininng shows how subtle they can be,
http://soundcloud.com/medusal-obligation/stgsequence-etude-ii
(And if you are interested in the MAQ, I’ve got one I’d sell. It works really well with the Voyager.)
playing non quantized tuned intervals
It’s all about the how you and your gear interface with it and what you can do. Some of it is certainly the challenge of getting it to do something you can’t with your fingers. Definitely some people go for the hands on with no computer approach. Then again one can get an interface connected to a computer and a some hardware sequencers are simply an interface connected to a dedicated computer inside the box. It’s not really cut and dry.
Back to your topic, control voltage definitely has a different set of capabilities and strengths compared to MIDI. Historically most people associate “sequencer” with a sequence of notes or to be more specific sequence of values representing notes. My understanding is the original term meant Sequential Switch, meaning a bunch of electric switches that trigger in sequence. You have one or more voltages (including on some gear audio) coming through each switch. Some analog sequencers are very plain and basic, but the more advanced ones offer plenty of options to do things like trigger changes to happen on a step or alter itself in various ways including using it’s own output to make changes to itself. One technique that definitely won’t fly with MIDI is running a sequencer so fast it creates an audio or LFO waveform output by itself.
Some sound advice here There is indeed a broad spectrum of sequencing options, from direct voltages to midi but all with hands on knobs. I guess some part of the fun is the accidental discoveries whereas as with a midi sequencer there are no accidents. Have to do some thinking about what I want. Might be time to justify starting a rack of modular equipment! That is a can of worms because I assumed I would get a euro rack of some sort, but all the purist analog sequencers seem to be Moog size.
Thanks,
Bryan