I flew ARN-CDG-SFO on a DL-ticket in AF P, and in terms of service, there was no difference at all. P Lounge access and no difference on board.
Mileage will be different depending on your program. For Flying Blue: A DL issued ticket gives distance based miles as opposed to spend-based miles for AF tickets. Further, your don't get UXP. The number of XP will be the same.