external battery cases for my iPhone 5s

Hi all,
So, as you know, my birthday is just around the corner, and my brother is planning to purchase me an external battery case for my iPhone 5s. I've red about the Mopie Juice pack air and plus, but I'm not sure which one is the best fit for me. they are both nice, but sometimes when I use apps and listen to my music, I usually runn my battery down to about 20%, then when I receive the low battery message, I plug it in to charge. My brother told me that having your iPhone pluged up all day heats up your battery. also, I'm a traveler, and I would like a case that has longer battery life, and that I could use while on the go. does anyone have any suggestions as to which case for my iPhone 5s offers more battery life from mophie? thanks a lot for your help.