As a member of a dual-program household (I'm AA Gold, former Plat; my partner is AS MVP), I'd say, like others, that both have their plusses and minuses. If you're primarily interested in redeeming miles for travel, AS is probably a better bet if you're based in North America, particularly the Northwest because of the broader partners. The low-tier elite (MVP) gets you a 50% bonus for every mile flown, which is twice as nice as the 25% bonus of AA Gold.

AA Gold gets you priority security lines when flying AA, which AS MVP does not when flying AS; that can be a significant benefit or worthless, depending on your travel patterns. AA Golds can upgrade companions occasionally; AS MVPs cannot. AA Golds do not have theoretically unlimited domestic upgrades for themselves; AS MVPs do. AA Golds do have pretty good upgrade success if you're willing to pay $30/500 miles.

If elite status on a worldwide network is your primary concern, AA is probably your better bet, as AA elite status earns you oneworld elite status as well. Platinum or Executive Platinum status gets you partner lounge access, which is very nice. (The DL reciprocal recognition of AS status helps, though.) If you're based in the Northwest and most of your travel is within North America, AS is almost certainly your best bet.

If you want to redeem miles when the lowest award level is not available, pretty much every frequent flier program out there only lets you redeem on their own metal. For example, AA miles can be redeemed for the last seat on any AA flight at twice the cost of the base (MileSAAver) award. I believe AS miles can be redeemed for any AS flight under similar conditions. Occasionally, that's nice to have particularly for short notice flights (I used the high level awards to get to a funeral that would not otherwise have been affordable, for example). In this case, you want your miles on the airline that's most likely to fly where you want to go.

AA allows one way awards (at half the price of a round trip; in fact, they no longer even have round trip awards per se), and AA awards can involve any number of AA's partners. AS awards are limited to one partner per award, and awards involving partners must be round trip.

I'll also mention that having one of us with AA elite status and the other with AS works well for us. When traveling together, we get at least priority boarding and free checked bags on AA, AS, and DL. (When I fly DL, I put the miles in an AS account, but I don't have to fly DL much.)

These are some broad ideas, but it's hard to give specific advice without any idea where you're based, what your travel patterns are, and what you want out of a frequent flier program.