Insane Battery Issues (4S and 5)

So I've had the worst trouble with battery life with my iPhone 4S (both my brand new version and the refurbished version I had to get after an experience with my phone taking a swim)... it would drain faster than you can imagine, even when doing nothing. I'd wake up with it fully charged, take it off the charger, and by the time I get to class (a 10 minute walk across campus) it'd be around 80% with just generic use: music playing, checking Facebook, Twitter, and Instagram, and some texting and checking email. That all isn't really that intense I don't think and it's literally only ten minutes of usage, and 20% of battery is gone. I was always having to charge my phone at least twice a day, and if I went away for long periods of time, e.g. to a football game, I could count on it dying before getting in or shortly after, and being without a phone until getting home to charge it.

All of this was one of the biggest factors in me deciding to get an iPhone 5 - so I did. I'm having the same problems. Battery is going quick, even when I:

• Turn off location services
• Turn off wifi
• Close all apps
• Have brightness very low and on auto-brightness
• Use the device lightly (e.g. just texting for a while)

I'm not sure if there's something corrupt with my saved backup or a bad app somewhere on my phone (don't know what it could be since the problem persists with all apps closed). I know the problem isn't a bad battery because it's been an issue on three phones now (two 4S' and a 5), or bad charging habits because my iPhone 5 is brand new.

I've tried all the generic suggestions and tips as explained above, and don't know what to do at this point.