seems like this is the thread to compare the Axxe vs. Prodigy, and since I now have both perhaps my opinion might be of value.
Prodigy; I have the early version w/out cv/gate etc. jacks in back, although I'll probably add them at some point. sounds lovely, leads and basses are stellar, the oscillator sync is fun, and the filter is, of course, what everyone really wants. it only has 32 keys though, which limits how far you can stretch out on an extended solo. it also has a quality feel to it that the Micro/Rogue/Realistic MG-1 lack. what the Prodigy does lack however, is versatility, if you need bloops, bleeps, and other FX they aren't here, unless you want use a Moogerfooger or two, which would really make this thing unbeatable. prices are hovering around $800 so add $4-500 in outboard gear (reverb/delay/ring mod/phaser) and be happy even if you can't get $5000 together to buy a Minimoog.
Axxe; just got the black/orange later version, won't match my Omni I but who cares? it's got all the fun stuff the Prodigy doesn't, Sample & Hold, Noise, lots of modulation options, and at 37 keys gives you a little more range without having to reach for the transpose switch. a ring mod would have been nice, but they were trying to keep costs down. seems like they did a lot of cost-cutting as the '70s wore on, I suppose someone had to pay for the cocaine & hookers, just too bad we have to spend so much getting these working again. prices are around $5-600 (less if you find one that needs repairs) and of course all the same advice about outboard FX applies here, although I'm happy with just a little reverb or delay.
if I had to choose I'd say the Prodigy had the edge for live use, and keep the Axxe in the studio, but you could easily swap the two depending on what kind of music you're playing. I like having both, better than trying to buy one synth that's supposed to do everything.