I think AI sells many more heads than speakers, so probably not many who have experience with all the cabs you are mentioning.
I have heard the original down firing AI speaker with the front pointing mid driver, but have not heard the newer designs. That original design was not my thing, but if that's the one you are talking about, it had a very different tone than the typical two way with tweeter tone of the Bergs you are considering. One of the 12/6 fEarful type boxes would probably be closer (although much louder and much more even and punchy). That organic top end of the mid driver loaded cabs, combined with the big low end extention of those extreme hi xmax subwoofer type drivers really results in a unique tone.
If you go to my iComposition site (listed as my homepage in my profile) there is a clip of a 12/6 (no tweeter)... that might give you an idea of the general tone. Lot's of clips of the AE410 also, which is in the general tone universe of the AE210 and AE112... bright upper mids, tight low end... mid punchy and aggressive.
I have not heard the HT112ER, but based on my experience with the original HT112, among the Berg cabs, either that or the HS210 would be more along the vibe of the warmer, organic AI cabs (again, at least the original ones).
Not really the direct, exact comparison you were asking for, but it's something
