IPhone: battery stick or battery case?

My iPhone 5c doesn't have the best battery life. I'm deciding between purchasing a battery stick or a battery case.
Each has their benefits. The battery case both protects and charges the phone but adds bulk. The battery stick allows me to purchase a real case, but it would be easy to misplace or forget at home.
Which should I get?

I use a speck case and a battery stick and works fine.

I personally use a Mophie external battery thing, because I like to have the protection of the case I choose.