I have a Samsung Galaxy S4 Mini phone, and the stock battery doesn't usually last me the full day. Do 3rd party batteries work well? Is there any battery that has a longer life than the stock battery?
As said in the comments, if you care about the battery life then look at the number of mAh the replacement battery has. The Samsung original battery for Galaxy S4 Mini is 1900 mAh so you want something higher, e.g. Zerolemon Samsung Galaxy S4 Mini 5100mAh. Beware that some batteries are too thick to fit in the original phone case, so they come with a thicker case. Also, there exist a bunch of applications that help detecting which applications take the most of your battery, you might want to optimize on the software side as well.