Let's start with a definition. Sharpness can either mean one of two things or some combination. We often term the meeting of the bevels from each side the "apex." But "apex" is a geometric term, and refers to an ideal with of 0. Nothing's perfect, edges have widths. What I call "absolute sharpness" is dependent on the width and consistency of the width of the edge itself. A very narrow edge, 1/1000", is sharper in that sense than one which is 3/1000". An edge which is fairly consistent at 2/1000" is sharper than one which frequently wanders from 1/1000" to 3/1000" and back.
The other kind of sharpness is "perceived sharpness," and that's the sharpness you feel. That includes things like polish, how true the edge is, acuteness of the bevel angle(s), symmetry, thinness "behind the edge," etc., etc.
Absolute sharpness is measured with a microscope and a micrometer, perceived sharpness with an onion.
Good sharpeners recognize that there's a tension between sharpness and durability, and frequently choose -- whether consciously or unconsciously -- to sacrifice a bit of one to gain a bit of the other.
There are some extremely good sharpeners in this world, people who can take a knife to whatever potential its alloy will allow. But most of us aren't that good. Most of us find that as long as the alloys we're sharpening have roughly equal edge characteristics, our own limitations will be more important than the identity of the alloy.
With that out of the way...
AEB-L sharpens as well or better than any stainless.
Assuming equal geometry, equally good heat treat, etc., an extremely good sharpener should be able to get White #2 sharper than 52100, and 52100 sharper than AEB-L, but that's not your typical sharpener.
White #2 has excellent strength and is better suited to extreme geometries than 52100, which is at least okay in that respect. Both are far better suited to extreme geometries than AEB-L, which -- comparatively -- sucks. If you're going to sharpen an 8* chisel, AEB-L is not a good choice. If, you're going to sharpen a V edge with 15* bevels and 60/40 symmetry, it's not going to matter much.
White #2 has an extra advantage in that it's one of the two most workable of the prestige Japanese carbons (the other is Takefu's V2S), and is used for knives whose geometry is so good they would be outstanding cutters if they were made out of folded beer cans. Their number includes inter alia nearly all -- if not absolutely all -- of the carbon lasers, and the Masamoto KS.
Everything else being equal, because it's strong, White #2 will be most resistant to going out of true via "impact burring." 52100 is not only slightly tougher but slightly stronger than AEB-L as well. AEB-L will need slightly more frequent truing than 52100. At typical hardness, you can steel AEB-L and 52100; it's a better idea to true White #2 (and any of the other YSS carbons) on a strop.
Tough steels wear slower than strong steels. All three alloys are strong AND tough. Of the three, 52100 is most weighted towards toughness, and White #2 most weighted to strength. That said, the ways different alloys wear, a counterpart to "perceived sharpness," tell you more about how often you'll actually go the stones.
Tougher to stronger: 52100 has better edge retention than AEB-L, AEB-L is better than White #2.
More nuanced: 52100 loses a little bit of edge quality very quickly, then holds onto what's left for a very, very long time. AEB-L loses its edge quality in discrete steps. White #2 holds its initial edge very well, loses a little quality, holds that a little while, then goes all to hell. White #2 is the more brittle of the three, and can be slightly problematic when it comes to chipping (and truing). None of them hold an edge as well as one of the really good powdered metallurgicals, though.
White #2 is the most sensitive to corrosion, and the most likely to lose edge as a result of the micro-pitting which comes from cutting acidic or corrosive foods. 52100 is much better in that respect, but no carbon can hold a candle to a stainless, and AEB-L is the best by far. The moral of the story is not AEB-L's superiority, but that you'd better rinse and wipe your carbon knives clean NOW. Not later. Goddammit.
I've prepped pineapple and pumpkin and split chickens with 52100 Ultimatum. No chips, no problem. But that's as much a function of the knife's weight and geometry as it is of the alloy. "George of Jungle say, 52100 good stuff. Knife abuse not good stuff."
Great question. No good, direct answer. Context. Context. Context.
Hope this helped,