I've done quite a bit of research on this recently and this is what I've found.

For the Citibank Dividend card, it doesn't matter if it takes you ten years to reach $10K in spending. Once you reach it, you should get your $100 check.

For the AMEX, the payout is as follows:

For everyday purchases, which includes purchases at stand-alone supermarkets, drugstores, gas stations and home improvement stores:

$1-$2000 spent = 0.50% cash back
$2001-$6000 spent = 1.0 % cash back
$6001+ = 3.0% cash back

For other purchases:
$1-$2000 spent = 0.25% cash back
$2001-$6000 spent = 0.5% cash back
$6001+ = 1.5% cash back

With these figures, the conservative estimate is that you need to spend at least $13K/year on your AMEX in order to exceed the flat 1% you can get with the Citibank card. This assumes that you don't spend any money on "everyday" purchases, which means the real number should be somewhat less.

One caveat with all of this. I've noticed that a lot of the credit card companies, AMEX included, have become substantially more vague in describing the specific cash back terms on their websites. In particular, I don't think you'll find any of this info on their web site. I suspect it allows them to do quick back-pedalling should they decide they're being too generous.