Like almost everything else you can build on AWS managed services (RDS, Elasticache, API Gateway/Lambda, Kinesis, etc), if it's truly critical to your application's uptime, you should be managing it yourself.
But if your need for ES is to support a backend system that would make your life inconvenient for a while if there are problems, is relatively small and won't grow too fast, but isn't business-critical, then the AWS managed service is fine.
But if your need for ES is to support a backend system that would make your life inconvenient for a while if there are problems, is relatively small and won't grow too fast, but isn't business-critical, then the AWS managed service is fine.