Okay, I can tell the difference between Winamp and Foobar playing that same file, after switching back and forth quite a bit. The difference, however, isn't that much, IMO. The only real difference I can really find is that there's a very much "crisper" sound when playing with Foobar, after I mess with them both to get the volumes to be about the same.
Anyway, now that I know what to listen for, I tried the iPod and iTunes again. iTunes still doesn't play the thing properly, but the section that it does play sounds closer to the Winamp rendition of the file, to me. The iPod plays it fine, but yes, it's closer to the Winamp rendition.
But the difference is anything but "obvious", in my opinion. It's very minimal, at best. The cymbal crashes have a slightly different kind of ring to them, and that's really about it as far as I can hear. However, like I said, I don't have the best hearing either.
Anyway, I didn't mean to be doing quality comparisons.

From the first few posts I was under the impression that these types of files wouldn't play at all on the iPod. They do play, but appearantly at a lower quality. That's all I really wanted to know.
Edit: Regarding file extensions.. If you leave it as "mp4" then iTunes loads it just fine, but strangely won't transfer it to the iPod. If you rename it to "m4a", then iTunes loads and plays it and will transfer it to the iPod. Also, iTunes will do the volume scan when it's named m4a but not when it's named mp4. The Sound Check volume equalizing adjustment then takes effect too, and the difference is easily noticable.