The long-running versions of reports can run for as long as the corresponding Lambda is allowed to, but will fail if the result is too big (this is a restriction of Step Functions). The standard reports can only run for 30 seconds but can return unlimited amounts of data. Some of the long-running versions omit extra detail so they don't fail.

Service Unavailable means the request ran for more than 30 seconds so API Gateway gave up. Report failed can mean that the report produced too much data.