As of Fargate platform 1.4, released on 04/2020, ephemeral storage is now 20 GB, instead of 10 GB. Additionally, you can now mount persistent EFS storage volumes in Fargate tasks.

For example:

{
    "containerDefinitions": [
        {
            "name": "container-using-efs",
            "image": "amazonlinux:2",
            "entryPoint": [
                "sh",
                "-c"
            ],
            "command": [
                "ls -la /mount/efs"
            ],
            "mountPoints": [
                {
                    "sourceVolume": "myEfsVolume",
                    "containerPath": "/mount/efs",
                    "readOnly": true
                }
            ]
        }
    ],
    "volumes": [
        {
            "name": "myEfsVolume",
            "efsVolumeConfiguration": {
                "fileSystemId": "fs-1234",
                "rootDirectory": "/path/to/my/data",
                "transitEncryption": "ENABLED",
                "transitEncryptionPort": integer,
                "authorizationConfig": {
                    "accessPointId": "fsap-1234",
                    "iam": "ENABLED"
                }
            }
        }
    ]
}

Taken from: efs-volumes in Fargate

You can now increase your fargate ephemeral storage to 200GB in task definition. Therefore with this there is no need to attach the volume unless you need a storage of larger than 200GB.

"ephemeralStorage": {
   "sizeInGiB": 200
}