Angels-high an F14 and F4 now thats an experience!
Although you have been in a wide variety of aircraft Flyer 1 I think there is a slight difference between being a passenger going for a ride than being the commander flying the aircraft from A to B and making crucial decisions when the sh*t hits the fan, that would be what I would consider experience. In saying that though im sure being in them and picking up a few tips from the the guy or girl flying, or even taking controll yourself for a while will do no harm at all.
Hope everything works out with the DA40 up in flightwise sounds like an impressive machine, at that speed though im not sure it would make a great training aircraft but i understand its for licence holders to fly. I know my heart would be in my mouth if a student was about to do his first solo in it