I do not know because I am not familiar with the 712s. But being a long time fan and owner of the k701s what headphone amp are you using?
The akgs 701 and 702s share a similar sonic balance. The 701 and 702s are fairly demanding of the driving amplifier powering them . They are very capable with the right amp driving them . I have strayed from using them at times but I keep going back to them. I have lcd 2 v2s but while the audezes have very smooth sonics I find that their soundstage reproduction is not all that great. When I want to hear soundstage I find that the akg 701 is vastly better at soundstage reproduction than the lcd 2 v2s.
Of the headphone amps I have I like the ray samuels raptor otl with it the sound is quite palpable with the k701s .The akg 701/702 headphones are quite amazing sounding with the right headphone amp driving them .And at the price you can get them at I think they are a astounding bargain .