Both headphones need power. Like, really good power from a speaker amp. I wouldn't trust any standard headphone amp excepting the Ergo Amp1 (for obvious reasons). Both headphones want several watts. The AMT likes 3watts or so, plus headroom. The K1000 more, perhaps 8watts, plus headroom. If the K1000 is amp fickle then the AMT is a complaining fusspot, as the Qualia 010 is oft said to be.
The Ergo AMT
needs one of it's matching amps (one is quite reasonably priced and also makes for a quite good headphone amp for normal headphones, the other is an expensive fully balanced class A monster with only the Hirschmann socket)
or the use of the impedance matching filter box
(one 8.2Ohm 5watt 5% resistor, one 0.18mH coil, one ELKO-glatt 35VAC 68uF capacitor, one ELKO-glatt 23VAC 8.2uF capacitor all in parallel per channel) (if i'm reading these parts correctly) I spent a lot of time trying to run it without this EQ box from power amps but it's never satisfactory enough. The removal of the box "cleans" the sound somewhat but the higher treble energy and lower bass energy that result is of greater detriment than having that thin layer of dust which is probably just a psychoacoustic effect of the difference in treble energy anyway.
K1000 bass goes a bit lower and has notably more weight, K1000 has more slam and weight to the sound, AMT has slightly less roughness or grit, or graininess in the mids and highs and is more accurate in representing the character of the resonance of piano and strings and the decay on prolonged notes or cymbals. Both project a good headstage, perhaps slightly more accurate in the AMT if you get the position right, the K1000 soundstage is probably always a little inflated, even with the drivers toed in just-so, unless you're one of the misguided that thinks that soundstage should be characterised by vastness and that bigger is better anyway. K1000 is very light, AMT is pretty heavy, but both are comfortable in their way. I'd say for me the AMT was the more comfy all in all despite the weight but the Ergo frame is unsuitable for those with very large or very small heads. K1000 has adjustable angle on the drivers, but once youve found the angle that works for you personally, you'll just whip it out all the way from time to time I suspect because once you find that angle that works for you, you'll want it left at that angle from then on. Similar for the vertical ajustment on the AMT (which is limited compared to the Ergo 1 or Ergo 2 because of the size of the AMT driver). AMT is
very sensitive to horizontal positioning because the driver pleats are gradual, larger at the back of the headphone than at the front and so bass output is stronger from the back. The design of the float principle is intended to take advantage of, nevermind mitigate, this apparently disadventageous transducer characteristic.
The design I'm working on for the AMT drivers does a great deal to mitigate its biggest flaw which is its rather weak bass output, the Ergo Amp2 is also designed with this as a factor when in combination with the Stock headphone. Precide spent years working on it. I haven't heard it but I intend to at my earliest convenience.
K1000 are easy to get a hold of, theres more than 12,000 of them, they're popular here and elsewhere and they're well known for what they are even outside of the hobby to an extent. The AMT comes up rarely on the used market, there certainly won't be anything like 12,000 of them but if you spot a set for sale that noone else has spotted theres a chance you may get a good price.
As for which one you should buy, that I can't help you with without more information from your end. Very different, and in some ways, very similar headphones. Both fascinating and both very good, but both difficult to get right.
See also these translations of a thread on a French hi-fi forum where there is a comparison between the K1000 and the AMT/Amp2 combo where both rigs are favourably rated and the Sennheiser HD600 gets a good kicking.
Here
and here