The difference is not much. iPhone has slightly better highs and slightly tighter lows. The headphones I'm using is Sennheiser MM70i (They use the same buds with CX400-II, I also have these).
I didn't found the difference with "critical listening". One night I just started listening it, and it sounded different to my iPhone. Then I played the same song on the iPhone and found out the difference.
The difference maybe due to different generations of DACs, different OPAMPS, different power budget, different decoders, etc. As I said before, the difference is not that much, but normal for the evolution of these types of electronics. Nano honestly sounds impressive for a device that compact.
P.S.: I used to play euphonium in a large band and double bass in a symphony orchestra, so I have trained my ears for separation and tracking of instruments and rhythm. This is why I'm a bit more sensitive to these things than most of the people around.
It's hard for our brain to comprehend that such a tiny gadget can sound so good, so I suspect that accounts for a lot of the perceived difference. Also, some music can sound better with a poorer output device by e.g. smearing noise in the treble or rolling off excessive bass.