If you are inclined, go to the App Store and download any of the free system monitoring tools that can display CPU usage. Here is the screenshot of my old iPhone 3GS about 5 minutes after upgrading to 5.1. You can see the CPU burning up at over 60%!
Here is another screenshot 35 minutes later. CPU is down to 8%, which is typical.
I see similar CPU usage on my 4S, also running 5.1. Battery life is fine. If your CPU is high, then start looking for CPU consumers. None of the monitoring apps I've seen can display CPU usage for each process, but if you experiment with turning various things off, you can use the app to see if the CPU usage drops. Maybe you have a rogue app burning up CPU in the background, something is crashing and restarting over and over, or push email is hammering your iPhone.
I hope this helps and good luck!