According to interviews he's the most relaxed manager most players have had. Rodgers used to fine players for all sorts of things, late for team dinner, late for training, not wearing team clothes etc. Laudrup doesn't have a fine system full stop.
After Liverpool last week, apparently it was the first time any of the players heard him raise his voice.
Who he is, IMO, has a lot to do with it. Not only is he one of the very best players of the past 20-30 years (for me, anyway), he also comes across as a likeable, down-to-earth person. That combination surely gets the respect of the players and thus his instructions are well received.
Compare that to Rodgers who is proving himself to be more and more deluded in his own thinking as each week and month goes by and you can see the difference. Oh, and he certainly ain't Michael Laudrup.