I have an old 3030 set (SR-303 headphones + SRM-313 amp) and I also have a pair of K1000. Keep in mind that I haven't heard the K1000 really well driven - say, from an expensive 300b tubed amp. For me, the main differences are:
- soundstage is obviously wider on AKGs; somehow, though, it seems to me a bit less cohesive than the "soundstage" projected by "normal" around the ear headphones like Stax or AKG K501. Anyway, it's a unique feeling, after K1000 anything else seems cramped
- both are very good at reproducing detail, but they focus on different things. The Stax reproduce ambience very well and allow you to head every instrument in a complex mix independent of each other. This makes listening through Stax a very easy on the ear experience. The music is coming to you in a relaxed, but persuasive manner.The AKGs have fantastic macrodynamics, they are like a fully charged sport engine, with sharp, precise attack and a very pure sound that emphasizes the texture of sound (like, you know, the "roughness" of the bow on the strings, as opposed to the resonance of the body of the instrument + ambient reverberations). Clear, spacious music in full sunlight.
- both are tonally on the lighter side, the K1000 more so (mine is a "bass-light" model, as far as I can tell). But if you can compensate for the brighter nature of the K1000 with careful system matching, the are very very good (better than the Stax by quite a bit) at reproducing the timbre of acoustic instruments! A cello sounds like a cello, a piano like a piano. This is their greatest strength IMO.
Hope it helps. IMO, YMMV etc.