1- Capacity: higher capacity means longer use time, if its for mobile phone, you can talk for more hours, and you can play more games, listen more songs Before you need to charge again.
2- Internal Impedance: High impedance can cause quick exhausting of power, itself can be a hidden reason of working current, the higher it is, the quicker the voltage will drop down.
3- PCB/PCM: Good performance of PCB can provide at least four important protections for the lithium battery:
Over charging protection
Over discharge protection
Over current protection
Short circuit protection
If the PCB sometimes can determine the safety of the battery system.