I own an FNX40, but I shot an FNP40 at the range, once.
The trigger is fairly light. I accidentally doubletapped off the paper first time I shot it after being used to my Glocks. It just felt so much like a Glock (similar overall weight and weight distribution, low bore axis, similar grip angle but without the hump), I guess I treated it like one.
The felt recoil is very soft and muzzle rise is minimal. I have yet to have a failure of any kind. It's currently the only handgun I can say that about, aside from my G21. I have nothing negative to say except that
1. the plastic trigger feels a tiny bit "bendy"
2. To detail strip it you have to remove the rear sight. ***.
3. The sights are made from some cheezy non ferrous die cast, or something. The paint wears off of them quite fast under normal use.
FNX only, not FNP:
1. oversize mag release is too big
2. depending how you grip, the control lever might jab horribly into the base of the thumb
3. Safety detent isn't positive enough for such a large, completely exposed lever.
4. If you try to decock it with your trigger finger high along the slide, the ambi lever pushes against your own hand.
5. Lever should really be metal and/or it should ride in a slight depression. For a lever that long and completely exposed, it's too flexible. You can catch the lever under a fingernail and bend it outwards, away from the frame, quite a bit. It has even been known to break off under normal use for lefties (right side lever is attached weaker than the left). Combined with problem #4, it's bad juju.