Yes this is a problem with the phone currently. People using wifi get stellar battery life, but if you use cellular data you will not. Anyone who claims days of battery life is using wifi and little to no use of the phone (even including overnight hours when the phone is not used at all in their overall time off charger). NO ONE and I repeat no one will get amazing battery life when using 3g or 4g only as their data connection.
I refuse to disable background data or cellular data with smart actions b/c I have a smartphone for emails and such for a reason. I do not have wifi access at home or work and have had much better battery life on other phones using cell data only on the Android platform.
There is rumor of an update in December that will help resolve data connectivity issues and battery life along with a few other bugs. Always rumor, but I am staking A LOT on it being true. VZW will not accept this from ANOTHER droid branded phone.