All of my phone last 4-5 times longer via WI- (no SIM card installed) than when on cellular data (e.g. 5-7 days between charges). That said, I'm at work, on LTE, with screen brightness just above 0%, with the phone charging on a 1500mA power supply, and my battery level is actually going "down" while running Jump Desktop (maybe pulling down 2MN of data per hour).
While I've always believed that the Note's screen was it's largest battery drain, I wouldn't discount it's "weakish" reception as a culprit. I've found that the Note will show (4) bars with only a -95dBm signal. Seems ambitious given that calls start to fail at -105dBm. Either way, at those levels, battery typically drains faster than when in better signal conditions.