AHD lumps -ence and -ency together deriving them ultimately from Latin -entia. Careful reading of the -ce, -cy, ... entry in Bingley's link shows that there are three varieties of -a/enc(e,y) words. Those that always or almost always end in -ce, those that always or almost always end in -cy and those that have both versions. The first two groups may have or may have had competing versions that never caught on or are rarely used and the third group may tend to divide up as Bingley suggested but you'll always be able to find counterexamples.