I think everyone probably knows by now where I stand on this subject! ;-)
I want the lot!
well - not exactly "the lot" - I have no interest in copying the sound of acoustic instruments.. I would see no point in making a theremin with sampling technology that could 'emulate' a violin or trombone..
I feel that analogue emulation of classic Theremins would be great - these could be presets.
I think that for historic reasons (if nothing else) we should, somewhere, have a full collection of samples of the RCA (both through its original speaker and from DI) and other rare / historic Theremins (some of the Moog Theremins definately need to have their sounds 'preserved')
Then I would want full control of the parameters making up the sound, so that everything from unique instruments to emulations of classic electronic instruments could be achieved.
If I was limited to a few tone paletts, I would be inclined towards sine - but I would definately want control of harmonic content as a function of pitch -
I think that, whatever "sound" one prefers, the sound (harmonic content) needs to change as the pitch changes.. even if this change is almost un-noticable.. without this, any and every sound becomes boring (or at least I think it does).
So I am being awkward again.. neither a,b, or c fits completely! - and I see no reason why we should limit ourselves to those choices.
For cost / simplicity, there are probably 2 main 'topology' choices -
The Moog EW whos sound is primarily formed by a combination of the distortion on its HF oscillators, its diode mixer, and its deliberate distortion added at the VCA - Its tone varies as a function of pitch primarily due to the fixed coupling between its HF oscillators which 'skew' the waveform.
The S/C Jaycar EPE Enkelaar type topology, which produces more sine-like waveforms - primarliy due (I believe) to the HF oscillators being 'cleaner', the fact that these HF signals are buffered by FET's prior to being mixed, and the fact that the mixing is done with a balanced modulator IC which gives less distortion, and provides more mathematically correct multiplication of the signals. These Theremins have controllable levels of oscillator coupling, so 'skew' can be adjusted - therefore harmonics change as a function of pitch - but you can control the degree to which this happens.
I prefer the latter topology, so if I must choose, I would say "b".
I have not seen schematics for either the tVox tour or the Henk Theremins, so I cannot say anything about their topology - but I love the sounds I have heard from these instruments.. I am not sure it is fair to lump these with the S/C and other 'sine class' instruments.
I am not sure that the PAiA fits in this 'sine' class - From what I have heard, I think perhaps it sits somehere between the EW and the 'sine' instruments.. but I have never played one, and have almost ignored this Theremin in my explorations.