I have Galaxy Note-I (N7000), and upgraded to Jelly Bean 4.1 today.
The battery drains fast. Do we expect any update from Samsung on the battery drain issue, or do I need to downgrade to ICS?
I used to own that same device and in my experience with several ROMs the best way to get a battery to not drain quickly was to switch to a AOSP rom like Slimkat/Slimsaber and to use adaptive brightness. The screen being 5"+ used to use a huge amount of battery. The stock Samsung ROMs are good but the AOSP ROMs make it a lot better in terms of battery usage.
Install "CPU Spy" in the Android Market -> Open CPU Spy and press Reset Timers -> Put the phone in to standby mode for a one minute -> then turn it back and check if the phone is gone in deep sleep.... If they did not go into deep sleep, then to turn off the phone and remove the battery for about 5 minutes, tell what happens ...