D6's keep it simple for newbie's; pretty much everyone can get ahold of those dice. I have thought that d10's might work for a less cinematic game, where 1 success is really hard to get, but then attributes REALLY start to outweigh skill levels.
That being said, I think it might be a good way to run bad guys minions as an optional rule. Was watching the Book of Eli last night where Denzel Washington was basically dropping a dozen bad guys without taking a scratch, and I realized that is NOT how AH's engine works. If you did want it to work that way, however, perhaps, bad guys roll d10's needing to get a "10" for success, while the "hero" needs to get 6's on a d6 platform. Just an idea...but I think AH would lose some of its simplicity, and therefore its appeal, that way.
Not that I've played yet, but I think that the Nameless Hordes! optional rule would probably be alright for minions, rather than using a different die. They would still pack a punch if they actually hit, making the game just as dangerous, but would go down easy with no need to track Health, provided they didn't dodge or block, which would really be their only defense. Even if you use the dodge/block reduces successes rule you still only need 1 success to pop one of the Nameless Hordes!.