Sorry to hear about your Samsung Galaxy S3 but its normal with Samsung smartphones. I myself own a Samsung Galaxy S4 but now it is giving very poor battery backup as compared to previous months. As you are planning to upgrade to a extended battery for your smartphone, then I would like to tell you some advantages and disadvantages.
1. Additional battery life before your smartphone dies.
In my opinion this is the only advantage to extend your battery size. Now take a look at the disadvantages.
1. To make these batteries available for everyone manufacturers use cheap materials in them. There is no assurance that for how much time you battery will work.
2. There are more chances of explosion than normal batteries provided in the smartphones. Extended batteries comes with more anode and cathode which may be lead to explosion of it. As it is a bigger battery then there will be bigger explosion as well and it will be big enough to harm you.
3. You will strain your charging port on your smartphone. Manufacturers limits the amount of electricity flows to your battery to prolong its life. Charging port of a smartphone is focused on battery provided by manufacturer. So there will be not enough flow to your extended battery which will damage it due to lack of power.
Till now you must have made your final decision on choosing about new battery of your smartphone. If you are suffering from battery drain issues then get your smartphone checked. You will need to get few things replaced on your smartphones such as charging port, battery, etc.
Normally battery draining is caused by faulty hardware in any smartphone. Apart from all these, don't overload your smartphone with applications and try to use Power Saving Modes provided in every smartphone out now.
If you really want to get extended battery life then go for any good power bank which will cost you same as a extended battery and will save your smartphone from damage as well.
I am currently pursuing High School and planning to pursue career in Computer. Currently, I work on one of my blog - JTech Articles.