I have had my moto x 1st gen for a year and a half now and my battery life is significantly worse than before. If I get a new moto x 1st gen but use my current SIM card, will my battery life be better?
Probably, but why are you getting reduced battery life? Finding the cause of that, and applying the fix, would be better.
This may help:
[Guide] The Care and Feeding of Lithium Polymer Batteries http://forums.androidcentral.com/showthread.php?t=500054