Mostly a pop and then slack. I know ropes can store an awful lot of energy, but every one I've ever broken has been remarkably un-eventful, so far as ropes whipping around and such.
Steel cable is another matter entirely, as we all know. Back when my dad was driving tow trucks and pulling wrecks out of the Salt River Canyon, he snapped the J hook off of 300 ft of cable. The whole length just swung 90° to the right, parallel with the road and wrapped up in the guardrail. It swept the slope completely clean, threw crap everywhere. Obviously there was an enormous amount of energy stored in that cable, and it had to go somewhere.