New iPhone 4S using 10 times faster battery than old 4, why?
It can be for a variety of reasons these include:

• Location Services in regular use, like Siri geofencing in reminders or a GPS app using it a lot. Check Settings > Privacy > Location services (in iOS 6) to see what's using it.

• A mail account that's not set up properly or had stopped working correctly from a restored back up, for example the outgoing mail server password not being entered on an IMAP or Exchnage account.

• Push mail being switched on. Settings > Mail > Fetch, to see how it's set up. 

• An app that's misbehaving and using a lot of CPU time (you may notice the phone warm up a little). Check your logs in Settings > General > About > Diags and usage > Diags and usage data, for anything unusual. Also check Settings > Usage - Time Since Last Full Charge to see if the time used makes sense, have you been using the phone for as long as it says? If the Standby time and in Use time are the same then something is running in the background. 

• Using the phone in a poor reception area will dramatically lower battery life, even in its on standby. 

• A corrupt restore from back up.

Things to do to try and resolve the issue:

• Power cycle the phone

• Reset user preferences. Settings > General > Reset > Reset all Settings. 

• Restore phone in iTunes and set up as new. (Most invasive option, but will sort the issue).