One situation where needing more 6 MP comes into play when you are taking long shots, and you want to crop in on one part of the photo and zoom in on the detail. If your lens can't zoom that far...
And yeah, you can see a definite difference between 6 MP and 24 MP in quality, although most of that gets tossed in the transition to 72DPI for web photos. Fine details in wood grain and such show up real well on the Nikon, where the Fuji would not quite catch the same level of detail. That's more a function of the sensor sensitivity I'm sure, but the 24 MP plays into it as well.
But as I said, the #1 reason I upgraded is that the Fuji wasn't nearly as good in low light situations (mind you, it was no slouch to begin with), and I'd have to augment it with auxiliary lighting or fall back on the flash (which would kill the ambience of the shot). I'm taking pics with the Nikon in the same lighting situation with no supplementary lighting whatsoever, and can even pull in details in lower light situations without nearly as much blur (if the subject moves slightly while the exposure time is elapsing). The Nikon doesn't require nearly as long exposure times...
Plus the Fuji didn't have anywhere near the shot buffer that the D3200 has. Important when you are taking rapid fire pics in succession, or doing movies (although I've yet to film a video on a DSLR, I do almost exclusively stills with these).
Oh, and MUCH longer battery life!
Short form, for the money, so far IMHO the D3200 is awesome. Almost grabbed the D3300, but the D3200 was a bit cheaper, and they threw in the 55-200MM lens to boot (grabbed it at Best Buy).