Can I use a iPhone 4S battery into a iPhone 4?

The issue is that I recently bought a used iPhone 4 for use it for work purposes, however, this phone is having a poor battery quality. It drains too fast I have to say, even thou I do all the things to avoid to waist the "energy". I have also a 4S for personal use an this one the battery will last all day with full use.

Then, I was thinking I just need to replace the battery of the iPhone 4 for a new one? or (if is because of the model, that the battery have a better performance) can I buy a 4S battery and put it into a 4?

Thank you very much.