Biiiiing-leeeeee---[KISS]
I think Bingley's going to win. B, you wrote:
how about -ence words show an abstract quality, and the -ency words show an instance of that quality in action. Thus, The judge's lenience was criticised by the popular press. We're talking about the judge's general attitude.

The defendant was grateful for the judge's leniency in sentencing him. We're talking about a particular instance.
X-refer says:
The Oxford English Dictionary defines lenience as 'lenient action or behaviour; indulgence', and leniency as 'the quality of being lenient',
For leniency, Merriam-Webster's Collegiate gives
1 : the quality or state of being lenient
2 : a lenient disposition or practice
For lenience, it just refers you to leniency!

If I may take mild exception to your The judge's lenience was criticised by the popular press. We're talking about the judge's general attitude. , I think the way it is worded here might be more applicable to a specific instance. If I wanted to talk about general attitude, I might write something like: The judge, being known for his leniency, was criticized by the press.

Oh, no! Look what I found in X-refer's page for -ce, -cy: it is unwise to theorize about the distribution of the rival forms without reference to the relevant Oxford English Dictionary entries. Ha!
I must say that I don't think the comparison of emergence to emergency should have been included, because the two have completely different meanings. Unless...DID emergency ever mean emergence? Would someone ever have said that they witnessed the emergency of the butterfly from its cocoon?