@According to this page your iPad meets the requirements (iPad Retina/4 isn't listed but it should be equal to the iPad 3).: as pointed out, the headphones you mentioned are bound to be driven by a dedicated amp, the AKG Q701 being the most picky of the bunch. The Fidelio X1 pairs well even with phones as long as your devices have a low output impedance.
The DT770 PRO and M50 are both bass-heavy, so the X1 might be the most similar to their sound. The HD598 doesn't have a whole lot of bass, so you might not like it. Q701 is fairly neutral but is pretty well balanced. The HD650 might have the most natural timbre of the bunch.
There is no "best" sound since that's influenced by personal preferences.
The DT770 and the M50 are known for their V-shaped sound while the X1 is pretty smooth with a nice hump in the bass region. I think that the Fidelio X1 shares more similarities with the HiFiMAN HE-400 and the Sennheiser HD 650.
Edited by MrScratch - 6/18/13 at 4:44am