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The iPod shuffle does play MP3 files, if that's what you mean by "convert". Using the same files and the same headphones, I don't expect you'd find much difference in sound quality. Apple generally gets good ratings for playback quality, but if you're using the standard little earbuds, your expectations can only be so high.
Yes most mp3 players put out pretty good sound quality. iPod is pretty good for this and getting quality ear-buds for under 100 bucks isn't too hard to find. Lots of the popular ones that sell right beside iPods and Shuffles on EBay are Shure E2C, E3C, Etymotic ER6, ER6-i (Supposedly made with iPod in mind), and the hardcore ER4's which are very expensive.
E2C is about 100, E3C is 180.
ER6 140, ER6-i 150, ER4 280+. Surf around for good deals on these babies cause they're supposed to sound delicious. I'm currently looking for some too.