Yes, aerated concrete also exists in different bulk densities.
Styrofoam always has a better thermal insulation effect than aerated concrete or any other stone, but it is not a stone and therefore an apples-to-oranges comparison.
In my opinion, the essential statement is that both wall construction alternatives fulfill KfW55.
KfW54 or 53 etc. do not exist. From a funding perspective, anything that does not meet KfW40 is considered only KfW55.
"Only" meeting KfW55 already means a good thermal insulation standard. Managing to save five euros more in energy costs per month somewhere else doesn’t make a big difference. I wouldn't want to adopt a stupid wall construction for that.
I have already slept as peacefully as in Abraham’s lap behind aerated concrete walls, noticing no poor sound insulation. Even when walking next to metalworking companies in aerated concrete halls, no noise disturbed me, although I have very sensitive hearing and there certainly was no monastic silence there.
My answer to the house provider’s question "would you prefer to plaster masonry or insulation boards" would be without hesitation masonry.
I summarize:
1) 12 cm Styrofoam insulates "better" than 12 cm more aerated concrete.
2) As long as the "KfW40" bar is not reached, it remains KfW55. Whether one could theoretically reach a virtual KfW49 with massive aerated concrete and a virtual KfW44 by substituting 12 cm wall thickness with insulation boards is irrelevant for funding.
3) How much of the calculated energy savings with "more insulation" actually ends up in the wallet is questionable. I see that as no more than peanuts.
4) Aerated concrete is neither a catastrophe in terms of noise and sound insulation, nor could that be gold-plated with Styrofoam.
5) Massive aerated concrete is dowel-stable on both sides.