How many widgets do you have active? Anna had a feature to turn off widget updates - can't find it in Belle. I turn off data when I don't need it - I'm not a keen face thingy user, so I don't need to be "up to date"
Wireless and bluetooth can chew battery - so you can turn them off to save battery. Drag the top bar down and you will get a screen which allows you (amongst other things) to turn things on/off. Turn off wireless (unless you really want it) and bluetooth (ditto). See how you go.
That sorts out battery - maybe your widgets are consuming CPU as well (ie. updating too quickly). Without a connection, they will be dormant. With a bit of luck, you might fix all your complaints
To give you an idea, my n8 is getting about 3 days per charge (going into power save at night). The performance is significantly better than Anna - no noticeable lag anywhere, so maybe the widgets are the difference. I still have my email widget - but it is in "offline" mode until I sync it.
Hope this helps....