It's probably not placebo. There are audible differences between players and it is also measurable. The Clip+ has to my knowledge the lowest output impedance of any portable player. This means the possibility of less to no frequency response variations between the source and headphones. The Clip+ also does not suffer from bass roll-off when it sees a low impedance headphone load. Many portable players suffer from this and it is again audible. The Clip+ I would guess would have higher max output/lower distortion than your phone as well.
