Using mosfets instead of relays for speaker protection - Distortion?
Am I correct in assuming that I should look for a mosfet with as
  little change in Rdson with Id? So not this one?... But rather this
  one:


The 320A (?) FET has much lower Rdson to much higher current than the 5A FET, so it would seem like the obvious choice due to its lower distortion and power loss. However there may be other factors involved such as voltage ratings, Gate charge, physical size and mounting requirements, cost etc. 

A specification of 'as little...' is generally not good design philosophy for a commercial product. Your 320A FET looks great, but there may be another one that's even better (and costs even more). When do you decide what is good enough? 

Once the resistance gets low enough to be 'inaudible', going lower is probably a waste of money - unless you can convince customers that the over-specified component is worth paying for.