I have been meaning to write a quick explanation on this for a while as I have seen a few (not many) kites getting tangled in the sky and they can get nasty if not handled correctly.
EACH SITUATION CAN VARY, but if you ever get 2 kites tangled in the sky you should de-power (let the bar go) straight away. This will kill the power as well as possibly save your lines. You should have your hand on the quick release – if it continues to pull then pull that as well. AND If it is still a problem then cut away totally – the situation can get nasty so be prepared and know how to disengage!
When a kite flies across your lines it can make your kite kite loop which can be very dangerous.
Lastly – if your kite crashes into another so it is your fault then you should be liable for all repairs – it is the right thing to do, but that is another story.