Complacence refers total self-satisfaction, while complacency referring to a feeling of contentment or self-satisfaction, especially when coupled with an unawareness of danger or trouble, has a wider use and be expressed also with the following expressions:
resting on one’s laurels:
- To be content with one’s present or past honors, accomplishments, or prestige. The laurels in this expression have long been a symbol of excellence or success in one’s field of endeavor. Resting indicates self-satisfaction and complacency with the implication that no further efforts will be expended to acquire additional figurative laurels. It is interesting to note that ancient philosophers and poets sometimes kept laurel leaves under their pillows for inspiration, a concept almost totally opposite to the phrase’s contemporary meaning.
snug as a bug in a rug:
- Extremely comfortable and content. This common expression of obvious derivation was purportedly used by Benjamin Franklin in 1772. The phrase enjoys frequent use in the United States.
Ngram, shows a wider usage of complacency.
Etymology:
Complacence and complacency have the same etymological root. The suffix cy was added later around 1640s when complacency come into existence.
complacence (n.)
- mid-15c., "pleasure," from Medieval Latin complacentia "satisfaction, pleasure," from Latin complacentem (nominative complacens), present participle of complacere "to be very pleasing," from com-, intensive prefix (see com-), + placere "to please" (see please). Sense of "pleased with oneself" is 18c.
complacency (n.)
- 1640s, from same source as complacence but with the later form of the suffix (see -cy).
-cy
abstract noun suffix of quality or rank, from Latin -cia, -tia, from Greek -kia, -tia, from abstract ending -ia + stem ending -c- or -t-. The native correspondents are -ship, -hood.
Sources: Etymonline.com/ www.thefreedictionary.com