I know this perspective is not relevant for most companies: But for side-projects and a-like the cold-start time for Aurora is like 15 - 30 seconds, and the first query always times out.
Having it always on (if just 1 "compute") will cost you 30 USD a month. I'm hoping for Aurora to eventually be closer to DynamoDB pricing and startup (I'm fine with 5 - 10 second cold start as long as it doesn't time out the first request everytime.)