Most powerful headphone amp?

As far as "raw horsepower goes" (which is a bad analogy), tube OTL amps have the most.  They can handle the voltage demands of high impedance cans.  However, while OTL amps are better at voltage, they aren't the best at current.  Lower impedance cans really benefit from lots of current.  I think for the 701/2, you would benefit from a solid state amp with very high current.

For example, in the speaker field, you often see 4 ohm and 8 ohm speakers.  The majority of speakers are 8 ohm and the majority of big store bought amps are low current.  Coincidence?  These lower current amps really struggle to power 4 ohm speakers, despite them being lower resistance.  To power 4 ohm speakers, you need to look for the "high current" amps.

Same for cans.  The tough drive low impedance cans, like the 701/2, will be best served on high current solid state amp, whereas the high impedance cans (like the 600 ohm Beyers), will probably be best served on tube OTLs.

Like all things, there are exceptions.

I'm using an OTL on the 701s and RS-1s with satisfactory results. The output is 500mw @ 20 ohms. AKG tech. data says 200mw max. but I'm am assuming that is continuous.

In the Cost is no object category, the Beta22 from AMB and the Dynahi from Kevin Gilmore (both DIY) are likely two of the most powerful solid state amps around. The Beta22 is capable of putting  out 18 Watts into an 8 ohm speaker load.  I'm sure the Dynahi is capable of similar power output.  They Hybrid EHHA (DIY again) is also capable of very high output current.  

From a bang for the buck perspective, the CTH (another hybrid) is amazing, capable of driving even Orthodynamic headphones, which except for the K1000, are probably the just about the most difficult headphones to drive properly.  I just sold one to someone who uses it with Smeggy's Thunderpants  (hand built headphones based on Fostex orthos) and loves it.

Dont forget the dynomite amp. 

Krell used to (perhaps still does) demonstrate the silence of their BIG power amplifiers by hooking them up to Grado RS-1 headphones. 

1Kw monoblocks.... indeed.

My Steve McCormack DNA .5 make a great head amp....