Poor signal = poor battery life.
If the phone is constantly searching for signal, it will affect battery life. This is why I leave wifi always on and connected if possible wherever I am. This only affects data polling of course but it still helps.
There aren't really many choices for Jellybean modems but if you are running a rom that lets you use ICS or GB modems, there are a ton of choices and it is trial and error what will work best for you in your area.