It sounds like you're asking 2 questions:
- Is an imbalance in motor performance indicative of a failing battery?
- How would you test for a failing battery?
The answer to the first question is "maybe". We had an issue on one of the AUVs I used to work on, where sometimes at the end of the day it would lose all heading control. By chance, we discovered that one of the motor controllers (used for differential drive) stopped working when it dipped below a certain voltage, where the other one waswere unaffected. So in that sense, the imbalance in motor performance was related to the battery but not necessarily a battery failure.
The best way to rule out the battery would be to tie your quadrotor (with only a few inches of freedom) to a table, and measure the battery voltage while you manually control it. Does it drop below what you'reyou are expecting, indicating an inability to supply enough current? Another way to do it would be to replace the battery with a simulated battery (variable voltage source + variable resistor) and test whether dips in the output voltage or increased internal resistance are to blame.
The answer to the second question is more complicated, but a decent resource for it is here: Testing Lithium-based Batteries
Essentially, you must measure the response times of the battery to changes in load.