Clean octave is mostly digital I'd say, especially if you're looking for polyphonic clean octave.
The warping/glitching mostly comes with analog stuff though.
To make the octave down even heavier I seriously recommend the
DBA Kill Kill Filter, now that can make almost any octave pedal sound heavy as fuck.
I tried a few, my findings more or less are below, in case it might help.

Analog Octave Down.
Aguilar Octamizer: no 2 octave down but running dirt into it brings on the heaviest lows I ever heard
Boss OC-2: lots of fun, the most synthy one I heard so far, nice and special
MXR Bass Octave Deluxe: between the Octamizer and OC-2, better tracking than the OC-2 but not quite as synthy sounding
Octave Down Fuzz
Catalinbread Perseus: nice sound and quite good tracking, mostly not very nasty or glitchy
Copilot FX Mantis II: the same nasty sound as the Seppuku only much more versatile and has better tracking
Electro Harmonix (Bass) Micro Synth: sounds great, lots of possibilities, nice filter too for making really synthy sounds
LAL Gomorrah: whatever
Seppuku Octave Synth: quite nasty sounding in a nice way, tracking isn't very good, not very versatile
Subdecay Octasynth: a bit like a Micro Synth in a small box, sounds really synthy as well, good tracking but can do some cool glitches too, setting the filter to open the way I wanted it was tricky for me though
Polyphonic Octave Down (digital)
Digitech Whammy 5: sounds great but the octave down could be heavier I think, I mostly use the blended octave down / octave up and the pure octave up modes
Electro Harmonix HOG/POG series: don't like any of them, quite a typical sound, either love it or hate it I guess