My dad uses the 5C, and his unit started to malfunction just like yours about 5 months ago. The Apple Store in his area told him that it is too difficult to replace the battery in the 5C, so for the price of replacing the battery, they gave him a "new" (a refurbished) 5C. I asked him how his phone is few days ago, and he says it still feels and works like a brand new phone. When his 5C goes "bad" again, it will be well overdue for him to get a newer model -- I mean he is on iOS 9; that's not safe anymore.
So, where is the replacement offer for 5C battery? Probably none. Is Apple going to do something for those who still like their 5C? You can ask your Apple Store to see if they will replace your phone for the price of the replacing the battery. Is Android the way to go? I think it is your best option, if Apple's policy upsets you.