It's nice not having a cable drag your head, but you have to put up with the risk of the battery going flat. In that case it's not just the ANR that stops, it's the whole headset, so you no longer have the radio. And since the batteries are built in, you can't whip in a new one quickly, you need to recharge.
I'm going to Ausfly and hopefully someone will be selling S1's or Bose A20's there so I can compare.
I know EQ1's will be sold there.