Unless it's for collecting purpose I don't see any other reason, because I got those carts (10x boxed) which play USA/JPN games on a European NES.
You won't get the extra audio that the FC is capable of, unless you mod your converter and NES. Using the FDS is workable, but awkward. Also, you won't be able to use any FC-exclusive additions (like the FB keyboard).
No, you really wouldn't need one unless of course like Ugly Joe said; The Famicom does have alot of interesting items built for it that NES never received.
I personally own a official toploading NES and an official AV Famicom because owning both just feels right to me, having both hardware units makes the cartridges feel more complete.
EUR NES is PAL (50Hz) and Famicom is NTSC (60Hz). The speed is the major difference. You won't get the right gameplay speed when playing Famicom games on PAL NES. You can check the speed difference using an emulator (like FCEUX) and tick/untick the "PAL emulation" when playing...
Platformers, point and clicks, and a select few RPGs.