Keep in mind 3g uses the most battery for your internet condition. WiFi and LTE are more efficient though your low signal on LTE wouldn't help.
We are on the fringe of LTE... Sometimes our phones connect to LTE, but is generally with very low reception. Essentially we live very close to a 3G tower, the nearest LTE tower is further away. So many times if you turn on LTE the phone will flip back and forth between the two. All that handshaking easily affects the power usage. So in my house here, until the other tower is upgraded, I will stick with 3G if/when i'm not on WiFi