C4's internal amp is powerful enough for full size headphones there's no problem there, your AKG Q701 are 62ohms which is rather low impedance for full size . The problem here talking to me about C4 is I haven't heard that DAP, there's very little information about it on the English internet. Therefore if I was to prattle on and tell you go ahead and spend $700 US on this player it would be like the blind leading the blind. I am reluctant to even comment on what I've read about it because I have not heard the player. Most threads that pop up here about C4 go unattended. yet we all hear it's very very capable.
The problem with CK4+ is it suffers a steep low end roll-off starting at 200Hz you lose sub-bass, it is effected only by the headphone out and not the players line out option, that's where the amp comes in. Even CK4 headphone out will run your AKG Q701 fondly I am confident on that because CK4 also has a seperate intneral amp but where this DAP is worth the money is by taking advantage of line out with a good
amp. If it was me? I would go for CK4 and see how it sounds with E7, if you're happy great if not upgrade to C&C BH which is my current full-time rig and blows most of everything I own away.
You can only buy these types of products on ebay and have them shipped internationally , these are not your average mainstream players. they're audiophile focused DAP's not everyone is interested in obtaining sound quality in this field so there is no point selling them retail because sales would be to low. If you want good sound you have to leave the mainstream, that's where we are now, guiding you to better sound quality.
Personally, if you want hi-fidelity sound you will never achieve such with a FiiO E7, you'd be better off putting up with the bass-roll off using CK4+ headphone out. Remember, some people love CK4 from it's headphone out, this is just my opinion on the player, I think it should be amped for best results.
You can read my take on Colorfly CK4 and C3 here.
http://www.head-fi.org/t/638415/colorfly-c3-vs-colorfly-ck4-comparison-true-portable-hifi-soundEdited by H20Fidelity - 1/20/13 at 5:49am