Can anyone tell me if I will collect AA miles if I book an Iberian flight through the AA website? The differene in price for business class IAD to MAD is $700 if I book it on Iberia vs. book the AA codeshare.

Do you mean that you want to book the AA codeshare or the Iberia flight number on AA.com?

Yes you do. (Please, American folks, correct me if I am wrong, because AA has plenty of strange rules and exceptions.) As both carriers belong to Oneworld, AAdvantage and Iberia Plus cardholders get miles / points, accumulate segments to match elite status, and so on, both in IB-coded or AA-coded flights. Identify yourself as an AAdvantage cardholder at the time of making the purchase (it's the safest way to have your miles credited) and check that in your boarding pass your FFP number appears bellow your name.

I didn't get if AA-coded flights were +700$ or -700$. Go for the lowest price. However, if IB gives you the lowest, I'd buy the ticket through iberia.com, since you'll have the opportunity to select the seat you want (only for Business Plus travellers, so... J tickets), and moreover there is a field for AAdvantage cardholders identification. If not, bear in mind that you can already check-in through iberia.com and print your boarding pass one day (or two?) prior to the departure, which will allow you to select the seat (only if the issuer of the ticket didn't assign one for you).

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Amazingly enough, American Airlines can tell you.

If Iberia is cheaper, I would actually price it through AA.com as well. Last time I bought a ticket, I remember saving $75-$150 because AA wasn't subject to some special tax applied on foreign carriers (I think). This applied even through they were only selling a ticket.
I was able to call them to assign seats.

Just for clarification, the Iberia website price of the tickets is $700 cheaper than the American codeshare booked on American.

Strangely, by choosing "show flights on all airlines" on the American website, it show the American codeshare flight at $3700+, and also the Iberian flight at $3000+ (the same price it is on the Iberian website). I assumed that if I booked it through the AA website I would have a better chance of actually getting my AA miles.

Thanks again for the tips.