I have an FNX-9 and I tried 135gr critical duty both the standard pressure, and +P rounds. Both cycled fine in my FNX. I have shot the entire box of standard pressure and 20 +P rounds. If have the money you should cycle 50 to 100 rounds before you start carrying it for CCW.
I carry 124gr Speer Gold Dot or 124gr Federal HST rounds myself.