I doubt your system is running slower due to a cheap battery. I could see the wrong battery being an issue or one that was bad (this is were a few cells are not working).
So lets dig a bit deeper into your problem to see if we can isolate the cause. First I would download this gem of an app: CoconutBattery paste a screenshot of the main window into your question here so we can see what it's telling us. Here's how: Adding images to an existing question
In the mean time did you calibrate your battery? This is a very important step when replacing a battery. Here's the steps: NewerTech - How to Calibrate a Mac Laptop's Power System
A common issue with this series is the HD cable can get worn and this can make the system appear to be running slower! Here's the IFIXIT guide to replace it: MacBook Pro 15" Unibody Early 2011 Hard Drive/IR Sensor Cable Replacement and you want to use the newer version of the cable: MacBook Pro 15" Unibody (Mid 2012) Hard Drive Cable. The area which wears the cable is on the rough surface of the uppercase. I place some electrical tape on the case where the cable rests.
Lastly, Hard Drives do need a bit of TLC! Over time the files get fragmented! Which slows their access as well as the systems ability to use virtual RAM space within the drive. I do recommend you yearly defragment your HDD. SSD are very different devices and don't need this. In any case I would first make a good backup of your drive with TimeMachine to an external drive before doing this.