I always use the EQUALIZER app to listen to music on the iPhone 4 and now the 4s - IMHO, it just sounds better across the board than the normal player, even without any EQ (I normally leave it flat, only occasionally giving a +2db 1.5q 44htz boost.)
I know some people like listening right out of the headphone jack - I can't do that unless I absolutely have to. I have a cheap micro LOD and the iBasso T3D and it's a drastic improvement over the headphone amp - the EQ app is also a slight improvement.
Sorry for not updating the initial impressions - the problem is, my LOD has gone bad and my backup is just this fiio LOD which is ok, but perhaps not really good enough for critical evaluation for such a discerning audience. My unnuanced take is that it sounds very similar - perhaps a tiny bit better, certainly no worse. I loved the sound of the 16gb 4, so I love the sound of the 64gb 4s that much more!
My desktop system (amarra 2.3 + yulong d100) is certainly more resolving, but not necessary any more euphonic on a lot of music, in fact, on anything that's compressed is generally going to sound worse.