I'm not sure how the battery performed, I bought it 2nd hand from ebay.
Does it really make a huge difference if I use a 3rd party battery?
Most of the time no. But you never know the quality of a 3rd party battery. I have seen pics of crap batteries that leak fluid.
When I bought a new battery for my old Blackberry off ebay, it worked fine.
If you bought the phone second hand, I highly suggest doing two things if you haven't.
Reflash using PC Companion (from Sony) to reinstall the newest software on the phone. And then when the phone starts up, go into Settings and Privacy and chose to do a Factory Reset.
90 percent of the problems I have encountered with all Android phones I attribute to something on the phone, not the hardware. So, if you think getting a new battery will do it....get one. Or find someone who has a phone with the same battery and borrow there's....see if it works any better.
I just think there is some junk on your phone or something that is setup that is drastically reducing it's battery life....that or you are playing a game that is very intensive on the phone.
Some games will completely waste the phones battery.
Even on my buddies brand new Samsung Galaxy S2, there is a racing game he plays that will only let him play for about 1 hour before it goes through more than 50 percent of his battery. Other puzzle games, he can play for 4 hours and it will only go down 25-30 percent.