Correct me if I'm wrong, but doesn't the "440" refer to the hardness to which it is hardened and tempered? I believe there are a number of different types of "stainless" steel. But I don't think "440 Stainless Steel" itself is something specific, only a somewhat generic description.
All AISI grades, such as "440 Stainless refer" to a specfic range of compositions. While there are many 'stainless' steels, each of them generally refers to a different composition, rather than a specific processing.
440 stainless, specifically, is a steel consisting of 16-18% Cr, 0.75% Mo, 1.0% Mn, a carbon content of 0.65 to 1.2% depending on specific grade (A,B,C), and balance Fe. Commonly, it can be annealed for a toughness comparable to a mid-carbon steel, or alternatively, it can be quenched and tempered to be extremely hard, but very brittle.
AUS-6 has much less chromium and a bit less carbon, and a kiss of nickel - I'm not 100% certain of the effects of nickel in steel, so these are informed guesswork, but, in comparison to 440 stainless, it will not hold an edge quite as well, but in return, it will be more difficult to break the blade.
From that, you want to match your material to your applications. If your knife is short, and you plan on mostly making well controlled cuts with little chance of blade twisting or leverage, then the 440 is your preferred choice. If you've got a slightly longer knife, or you expect a higher need to survive being twisted or bent, then the AUS-6 knife may have a longer lifetime.
The extreme case of this, of course, is the sword, where the lateral and torsional abuse rate is extreme, and stainless steels generally become lackluster at best or hazardous to the user at worst, due to the high chromium content reducing the ductility and flexibility of the blade.
verkill:
