I have booked AF PV seats on delta.com over the past couple years. The trick - and someone here taught me! - is to search for Y or above - NOT W. For whatever reason, if you search W or above, you only get first class on domestic legs -whereas if you do the search on the AF site, you typically get coach. Using Y or above in the advanced search feature can usually duplicate a fare found on AF. Now granted, sometimes it takes a while - but it's a personal challenge to me to get delta.com to work properly And I'm booking leisure travel so I don't mind waiting....

(unless of course you want first class on domestic legs, but booking Y on the domestic legs has gotten us almost instant upgrades on most of our flights but not all)

I tend to prefer to book on delta.com and stay on the 006 ticket stock as much as possible, though in case I am not able, I do appreciate MQD availability when booking on af.com. I just wish so much math wasn't involved