There is nothing special about the AAdvantage AMEX or HHonors (any more). You get the miles or points that you would normally get for using the card anywhere (through the card), and totally separately you get the miels or points or cashback with the Rewards Network dining program you use.

And you can mix them in any way that you want. Ie, you can earn AA miles from a card while earning UA miles through RN. You can earn Best Western miles from a card while earning Alaska miles thougn RN (I just did a dine like that the other day, because Best Western has no dining program and I have no Alaska card, so it was a reasonable match!).

The only thing that was special about the HHonors AMex at one point is that it used to give extra points at restaurants. So some people liked to use that. However, whether that math really made it worth more than miles or not then, the fact is that extra earning is gone, and now HHonors Amex earns nothing more at restaurants than anywhere else you shop.

The only card that earns more at restaurants right now that I'm aware of is Discover, and that's only if you register and only Oct thru Dec 2009 (Discover has rotatating extra-cashback categories) and it has a cap. But beware: Some restaurants that take Discover don't give miles for Discover, so if using Discover be sure to check the website for each particular restaurant as to whether you'll get miles for Discover, rather than using Discover automatically because you saw the logo at the restaurant.