*Silverback gorilla lumbers into the room*
For me, the absolute most critical thing is for a comp to have a linear, easy-to-use threshold control, with an LED or other indicator to show when the signal is over the threshold. The control and the indicator can take a wide range of forms, but when they are missing or inadequate, I am generally not happy (unless the tone by itself is "all that", like with the Effectrode). I've even thought about kicking the Demeter off my top picks list for exactly this reason. It was one of the best in its day, but not any more.
The fact that most comp pedal builders leave off what I consider to be the absolute most important feature of any compressor just baffles and annoys me to no end.
Pursuant to the usefulness of the threshold control and indicator, the input stage should accept a wide range of signals, from the quietest to the loudest (i.e. from a low-output vintage guitar all the way to high-output '90s active bass with a baboon slapping on it).
Everything else is gravy, and all comes down to personal tastes.