Interesting question as it is posed in the abstract. Aogami = blue steel. Blue steel comes in many elemental proportions. Nonetheless, even if you meant Blue Super it all comes down to sharpening skills. You bring a double bevel HD steel blade @Hrc 61 to an absolute 24 degrees included & a Aogami Super @Hrc65 to the same... is there a difference in "sharpness".?! I think not. And what is "sharpness," you may find a KonoHD @28 degrees included feels sharper than a thicker MoriAS @the same angle.?! Different geometries feel differently.
AS can be heat treated to higher hardness allowing more acute bevels w/o carbide fallout. Can a high Hrc Aogami Super be sharpened to more acute bevels than HD2 & not collapse... yes, but do you really want a 20-18 degree included angle double bevel on your kitchen knife.?! I W/O DOUBT OR QUESTION DON'T... in almost every application.
HD steel gets sharper than I ever need. I get my knives too sharp. "Too sharp".
.. how dare I claim that to be.?! Look... as a host cooking at their home under the stress of a party for 15, as a Chef de partie blasting through pounds of product for a 300 head rush, as a Sous Chef catching flak from his Chef de cuisine who has a Butler or an Expediter or a Proprietor or a Guest or a Principal up his ass for an order or about a menu revision or about the cook(s) that no showed, or as the CHEF (de cuisine)
with his job on the line with 150 VIP guests expecting nothing less than perfection over 5 courses... you are operating at a level in which the an ultimate edge that can "treetop" hanging hair is dangerous. Things are moving at a frenetic pace, and there can be "too sharp." The single largest thing that I miss about using soft steel is the ability of using my finger nail on my guide finger. On sharp JK's with thin spines that is not even the merest of possibility, and I do miss it. I find pleasure picking up my Wusthofs and crushing through product... just cause it requires such little focus. Are they sharp... of course, but the blade thickness & geometry is a totally different experience... much louder
Now, in the broad sense, HD steel @Hrc 61 sharpened to the same angle as AS @Hrc 65 is not going to have the same edge retention, but all of this is somewhat in the abstract as every blacksmith has a different heat treat which produces different characteristics. There is truly and honestly such a broad matrix to the question you pose that, in fact, it [said question] has as many variables as the moon's gravitational pull or the heat of the sun or the mood you are in.
Konosuke HD steel gets stupid sharp. It get's stupid sharp - stupid easy. It stays stupid sharp for a very respectable amount of time (that concept opens up the dynamic of fresh edges & working edges & dull edges), and its basically stainless.
Hitachi Blue Steels gets stupid sharp. Gets stupid sharp quite easily, and they stay stupid sharp depending on heat treat.