I think I've worked out the source of my poor battery life. I think it's because of poor signal at home. My iPhone and previous samsung phones were all on O2. At home I get a good signal on O2, however my boyfriend has never been able to get a signal with three at home. My note is unlocked but I've got a three PAYG sim in there. I think I'll just put it into aeroplane mode while I'm at home but leave wifi on and that will stop it looking for a cellular signal and should reduce battery drain.
That's how my battery life used to be with AT&T. My phone would drain to 50% in 8 hours because AT&Ts signal was so bad at my house and still is today. Once I switched to T-Mobile, with that same phone back then which was a 4S, the battery would last nearly two days. People don't realize how bad reception can affect battery life.
Does your carrier allow Wifi calling?