Well, SOS is citing Elektron in that article; they point out this “enhanced bass” in the FAQ on the AK. I have the AK, haven’t heard the A4 in person. I can tell you that the AK can get very… funky. (I believe you’re using this word to describe crunchy/distorted/lo-fi, etc.)
As per the differences in the various demos/videos/etc. some of that could just be that the workflow of the two instruments leads to different results. When I sit down at a keyboard, I think of melody; for a groovebox (which is what the A4 seems like to me–and I don’t mean that dismissively, because it is a glorious and comprehensive groovebox that would put the grooveboxes of yore to shame), I think more about rhythms, arpeggiated sequences, and patterns. That’s not always true, but I do think that the two workflows lead to different results. So I think the fundamental question is workflow.
Again, I cannot speak to the A4 directly, but the bass on the AK is very, very deep. I sometimes wonder if I should have gotten the A4 (especially, as has been noted, because of the way that OB mitigates the benefit of the individual outs), but the joystick is an insanely useful performance/creation tool, and I needed a solid keyboard in my lineup, so I don’t ponder it too often. But it’s not because of sonic differences in the two machines; it’s because the workflow of the A4 might be better suited to my tastes.