I'd go with a CZ 75. Practically any model would work, but I'd go with a CZ 75 SP01 Tactical -- which has a longer barrel than the standard 75B. It's my next handgun, for just about the same reasons you gave -- I've found I like target shooting and I'd like a pistol that is better at it than my FNP9. There's nothing wrong with the FNP -- but it's a personal defense pistol, not really one for target shooting.
If you really wanted a target-shooting pistol you might look at .22 LRs. I'm also thinking of a Ruger Mark II or III.
Good luck and let us know what you decide.