There are some differences. Graphics and soundtrack are different. The Wiiware version has a more classic SNES look. The PSP version doesn't have the RNG exploits to get rare items to drop quickly. Also, I think some of the tales might of been split up differently, though I am not totally sure of this. Two advantages that PSP version has: The new opening CG intro and the extra super boss, Lost Babil.
I thoroughly enjoyed the Wii version and all of it's RNG exploits, so personally, I would go for the Wii version. I only got to play the interlude on the PSP version, and I'm glad I played it, but it was short and you won't miss much by skipping over it.
I don't know how the saves work on the PSP, but it's nice having a dedicated file for each chapter on the Wii.
I had this incredibly, unbelievably, amazingly, fantastically directionally-challenged guy with me right here... http://i.imgur.com/p0ZKo.png
I can't believe there are people voting for the Wii version...
Yes, the RNG exploiting is gone, but that was only the result of sloppy coding.
Even without interlude (which is like 3 hours tops), the PSP version is utterly perfect - beautiful graphics, 2 soundtracks (original or enhanced), bonus enemies in each tale, bonus superboss, less randomness with the loot earned in challenge dungeons...not to mention for the price of the complete WiiWare game you get FF IV, Interlude, and After Years.
The thing I loved about the WiiWare version was during the summer of 09 waiting for each set of tales to be released, that was very enjoyable but it was a "had to be there" scenario.