The Fast Track at LHR T3 is not open in the evening (I'm not sure what the hours are at the other terminals now, but suspect they are similar), so I don't think the passes are given out on the morning departures ex-US. (Immigration queues when those flights land tend to be relatively short.) IME Fast Track is usually faster, except when there's no backup from an earlier flight in the Immigration Hall and all the non-EU pax from the front of the plane head over to the Fast Track queue, with no one in the "Other Passports" queue.
CDG now has a fast track for departures, but I don't know if they've added one for arrivals.