It will be dependent on multiple factors.
1: Whatever your game is, it could be too big for your phone to handle.
2: Firefox could be doing background processes when you start it. (Unlike Chrome)
3: Your phone is just bad.
4: (Previously Stated) Programs could be running in the background slowing down your device.
I would recommend downloading CCleaner and cleaning out your device then check for any updates you have not installed as they can be slowly taking CPU power.
TL;DR - Both your Phone and Firefox (probably)