Arcanepaths,all of the advice above is spot on,and thoroughly covers the jist of your question.
To add a bit of detail,for what it's worth:
The Hardenability of any steel alloy is a product of isothermic reaction of iron,Fe,and carbon,C.
In Addition to that people have learned to use other alloying elements,such as Chromium,Vanadium,Molybdenum,et c.,to further alter the physical qualities of the resulting alloy.
These other alloying elements bear on innumerable aspects of an alloy,but for us as woodworkers one specific difference is important,and this is how the "plain" carbon steel differs from the more complex alloy:
Simplistic,primitive way of looking at the hardened steel is where the soft,viscous,tough Iron matrix contains/holds/retains hard particles,Carbides,much like soft cement mix contains hard pebbles and sand grains.
In the case of Plain,otherwise unalloyed steel,those hard grains are Fine,very small as compared to higher-alloyed steel.(it is actually visible under(significant)magnification).
Because of their size the edge of your tool is a thin ragged edge much like a fine-toothed saw.
At contacting the material that you're cutting these fine jagged teeth immediately penetrate into it,with very little force necessary to effect that penetration.
In English,your cut has begun,and you can now rearrange your muscles to just control the tool's passage through the material.
Conversely,a higher-alloyed steel(most notably Cr based,which is nearly everything),has Carbides that protrude out of the edge that are Much larger;like the size of gravel used in your concrete mix has been increased.
These carbides look like large,rounded boulders(vs plain C alloy's ones),and take more effort for you to sink them into material and to maintain that continuing penetration.
So,in effect,it can be said that the higher-alloyed steel edge can never be as "sharp" as a plain-carbon edge.
Obviously there's All sorts of obverse sides to this medal,like the amount of work that plain C steel can accomplish between sharpenings and on and on...
But to some users(butchers,notably among these),this principle is important enough to put up with the lack of corrosion resistance,necessity for frequent dressing of the edge,et c.
Now,an axe is a specific tool,and the axe in question here is Very specific,it has a given,pre-determined edge geometry.
The angle of that edge is not that fine(relatively speaking,as compared to a butcher knife,a straight razor,scalpel et c).The mass of the tool is also greater.
So the described effect would be less obvious,less Felt.
And that brings us back to why the alloys used in axe manufacturing were historically uncomplicated,and thus also back to the solid common-sensical advise from the community above.
But,in some Very minor(if not microscopic)sense,a 10xx series alloy(in AISI system of designation 1 is code for Carbon as the main alloying element)edge will cut "easier",be easier to maintain the depth of cut,"grab" the wood readier than the edge of O1 or 5160(both Chrome-based alloys,way in excess of 1+% of C).
They'll have this tiny tendency to slide,to skate,on the medium being cut.
