It seems to me that the AKG K701 headphones are inverted but the Sennhieser HD650 headphones aren't inverted.
George S. Louis
what do u mean inverted?
The headphone diaphragms move in response to a positive electrical signal when they should be moving out, and move out when they should be moving in when they receive a negative electrical signal. If they were speakers it would be as if the red and black wires were reversed at the rear of both the left and right channel speaker. You may go to my website for more information about polarity and on the homepage click on the think piece about polarity and "The List".
George S. Louis, CEO
Digital Systems & Solutions
The K701 definitely needs an amp, as does the HD650, you don't need a great, expensive amp, a $100ish or even cheaper amp will do the trick but you will get better results as you scale up the price ladder, for diminishing returns.
The K701 sounds like a better match for you.
Recently sold the HD650s and bought the K702 (same as 701 but with detachable cable). Best thing I ever did. 702s have great mids and are very neutral across the board. Sennheisers are bass heavy, sluggish, and have recessed mids.