I've not seen any mention of ActiveSync on this thread so far.
My S3 is a work phone. One of the reasons I have got it is to access work E-mail so ActiveSync is essential.
Since moving to Jellybean, My phone has discharged to 30% by the time I have got home. I have tried reducing the sync frequency but this does not appear to have had an effect.
Is there anything else I can try other than to switch it off, charge it then charge it again?