I'll share my experiences with the D3, but I haven't flown non-rev since 9/11, so this may have changed.
First, I've found flying non-rev generally to be not worth the effort. Nothing is more frustrating than sitting at the gate waiting to see if you will get a seat, only to encounter a revenue passenger showing up at the last minute, possibly taking your seat. Then, once you DO board (IF you get a seat), you'll generally find no overhead bin space, so your bags end up getting checked. (Remember, you're flying non-rev, so complaining about it is not a good idea).
My wife and I tried to fly on a D3 to LAS from MIA, and we ended up having to spend one night at DFW after being denied seats on full flights over and over again. When you think of the loss of one day of vacation, plus hotel, plus cab fare, that D3 doesn't seem worth it.
That's the bad news. The great news is, if you want to fly International and you're not in the middle of peak season (non-rev travel is blocked during parts of the year), great deals can be had. We managed to fly F RT MIA-CDG and we paid about $200 total for the two of us. I'm told it's not a cheap ticket!
One word of advice: if you want to fly F as a non-rev, you need to be meallisted 48 hours in advance. Otherwise, even with room in F, they won't give you the seat. You can
call AA reservations during non-peak hours, just tell the agent you're a non-rev and you want to be meallisted for flight x on date y.
Last thing, post 9/11, the employee giving you the D3 needs to furnish AA with your passport number or other ID prior to your showing up at the gate, I'm told.
Bottom line -- in my experience, flying domestic on a D3 is a waste if you can plan the trip in advance. Long-hauls can pay off nicely, but only if you know the flights are not overbooked.
DK