I have an iPhone 5 and love it absolutely to death. It's the one thing I am extremely careful with, it's always in a case, always has a screen protector on it etc. It lives in an otterbox. I wouldn't swap it for anything... My bf has a galaxy s4 and has had no end of problems with it, it has been sent away for repairs several times and keeps coming back with the same issues.
And like PrivatePilot said, you can control what apps use your data, or you can switch off the option and then certain apps will only use data through a wifi connection. I only have 500mg of data, and the facebook app sucks a lot of that, so I often just turn facebook off through data, and leave other smaller things going, then I can still receive iMessages because I haven't turned off all my mobile data.
My only complaint is having to charge it every night, but I use it a lot, and I mean a LOT so I really can't complain about that. However, it does charge really fast... Unlike my bfs s4 which takes forever!!
My friends iPhone 5 has the same issues the OPs is having, but she hasn't bothered to get it fixed or replaced.
R.I.P ~ Bubbles - 25yo tb mare - 13.04.2011 ~ 8:30am ~ passed away naturally and peacefully in my arms