The FNX handguns have interchangeable backstraps, and a more aggressive feel to the grip of them. Other than that, I dont think there is any difference.
FNP: There are two models. Standard and USG (US Government). They both come with two back straps and three mags. The standard model has no front slide serrations, and is decocker only. The USG has a decocker/safety. You can get them with a matte black or matte stainless slide. The USG can also be had with a FDE frame.
FNX: Comes with four back straps and three mags. There is just one model, because they all come equipped with decocker/safety. They very much resembles the FNP45, its controls are different from the 9 or .40. Two minor things that I do not care for on the FNX. They relocated the magazine catch. Inserting a mag feels sloppy on some of the ones I have handled. I know some people reported having difficulty inserting mags when they where first released. I also do not like how the back strap is held on, compared to the FNP.
They are both great platforms. I own a matte stainless FNP9 which I absolutely love. It is my full size carry gun. I have shot Sigs, Beretta's, and other hammer fired platforms. However, the FNP just fits me, and is very accurate. I also have a matte black USG in .40. Which I'm trying to sale, only to consolidate calibers.
That was really my only complaint on the FNX 9 that I had. I didnt have any problems with the back straps, but I think over time, that system may not last.
The only reason I got rid of mine was because I didnt want a full size 9mm anymore. I also give FNH two