As Aura is always running the very latest version of the core database, you need to always use the latest version of the database available for on-premises to ensure you can successfully load the backup files you have exported and downloaded from your running AuraDB instance.

At times - usually very near a new major release - we may have Aura using the very latest store format for the database, and this means it would only load locally with the pre-release that we make available here: https://neo4j.com/download-center/#prerelease.I

Remember that you should set in neo4.conf :

dbms.allow_upgrade=true

If you use an inadequate version, you may see this message on the startup of your local instance (debug.log):

java.lang.RuntimeException: org.neo4j.kernel.impl.transaction.log.entry.UnsupportedLogVersionException: Log file contains entries with prefix 2, and the lowest supported prefix is 3. This indicates that the log files originates from an older version of neo4j, which we don't support migrations from

Loading locally to containerized environments:

If you are loading locally into a Neo4j running in a containerized environment like Kubernetes or Docker, please note that restarting the container is the simplest way to force the Neo4j service to pick up the newly imported DB.
The complete sequence, in this case, would be: 

1. Start the container
2. Connect to the database through the browser
3. Stop the neo4j database - STOP DATABASE neo4j
4. Complete the import operation.
5. Restart the container
6. Start the neo4j database - START DATABASE neo4j

Further troubleshooting:

If, despite trying this version, you still have issues loading the backup file, please ensure you attempt to load the backup with the verbose flag and share the full output in your support ticket:

bin/neo4j-admin load --force --database=neo4j --from=neo4j.backup --verbose  

The full logs for the error when trying to load and start the database:

2021-06-07 08:51:56.076+0000 WARN [o.n.k.d.Database] [neo4j/abcdef01] Exception occurred while starting the database. Trying to stop already started components.
java.lang.RuntimeException: org.neo4j.kernel.impl.transaction.log.entry.UnsupportedLogVersionException: Log file contains entries with prefix 2, and the lowest supported prefix is 3. This indicates that the log files originates from an older version of neo4j, which we don't support migrations from.
at org.neo4j.kernel.impl.transaction.log.files.checkpoint.DetachedLogTailScanner.findLogTail(DetachedLogTailScanner.java:101) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.impl.transaction.log.files.checkpoint.AbstractLogTailScanner.getTailInformation(AbstractLogTailScanner.java:241) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.impl.transaction.log.files.checkpoint.CheckpointLogFile.getTailInformation(CheckpointLogFile.java:185) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.impl.transaction.log.files.checkpoint.CompositeCheckpointLogFile.getTailInformation(CompositeCheckpointLogFile.java:105) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.impl.transaction.log.files.TransactionLogFiles.getTailInformation(TransactionLogFiles.java:103) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.recovery.Recovery.validateStoreId(Recovery.java:410) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.database.Database.checkStoreId(Database.java:571) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.database.Database.validateStoreAndTxLogs(Database.java:534) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.database.Database.start(Database.java:419) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.dbms.database.AbstractDatabaseManager.startDatabase(AbstractDatabaseManager.java:187) ~[neo4j-4.2.6.jar:4.2.6]
at com.neo4j.dbms.database.MultiDatabaseManager.forSingleDatabase(MultiDatabaseManager.java:141) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.database.MultiDatabaseManager.startDatabase(MultiDatabaseManager.java:119) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.Transition$Prepared.doTransitionAction(Transition.java:101) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.Transition$Prepared.doTransition(Transition.java:88) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.doTransitionStep(DbmsReconciler.java:355) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.doTransitionStep(DbmsReconciler.java:356) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.doTransitionStep(DbmsReconciler.java:356) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.lambda$doTransitions$12(DbmsReconciler.java:324) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.namedJob(DbmsReconciler.java:335) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.doTransitions(DbmsReconciler.java:325) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.lambda$doTransitions$10(DbmsReconciler.java:310) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at java.util.concurrent.CompletableFuture$AsyncSupply.run(CompletableFuture.java:1700) [?:?]
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:515) [?:?]
at java.util.concurrent.FutureTask.run(FutureTask.java:264) [?:?]
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1128) [?:?]
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:628) [?:?]
at java.lang.Thread.run(Thread.java:834) [?:?]
Caused by: org.neo4j.kernel.impl.transaction.log.entry.UnsupportedLogVersionException: Log file contains entries with prefix 2, and the lowest supported prefix is 3. This indicates that the log files originates from an older version of neo4j, which we don't support migrations from.
at org.neo4j.kernel.impl.transaction.log.entry.LogVersionSelector.select(LogVersionSelector.java:59) ~[neo4j-wal-4.2.6.jar:4.2.6]
at org.neo4j.kernel.impl.transaction.log.entry.VersionAwareLogEntryReader.readLogEntry(VersionAwareLogEntryReader.java:94) ~[neo4j-wal-4.2.6.jar:4.2.6]
at org.neo4j.kernel.impl.transaction.log.LogEntryCursor.next(LogEntryCursor.java:53) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.impl.transaction.log.files.checkpoint.CheckpointLogFile.findLatestCheckpoint(CheckpointLogFile.java:114) ~[neo4j-kernel-4.2.6.jar:4.2.6]
at org.neo4j.kernel.impl.transaction.log.files.checkpoint.DetachedLogTailScanner.findLogTail(DetachedLogTailScanner.java:68) ~[neo4j-kernel-4.2.6.jar:4.2.6]
... 26 more
2021-06-07 08:51:56.084+0000 ERROR [c.n.d.DbmsReconciler] Encountered error when attempting to reconcile database neo4j to state 'online', database remains in state 'offline'
org.neo4j.dbms.api.DatabaseManagementException: An error occurred! Unable to start `DatabaseId{abcdef01[neo4j]}`.
at org.neo4j.dbms.database.AbstractDatabaseManager.startDatabase(AbstractDatabaseManager.java:191) ~[neo4j-4.2.6.jar:4.2.6]
at com.neo4j.dbms.database.MultiDatabaseManager.forSingleDatabase(MultiDatabaseManager.java:141) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.database.MultiDatabaseManager.startDatabase(MultiDatabaseManager.java:119) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.Transition$Prepared.doTransitionAction(Transition.java:101) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.Transition$Prepared.doTransition(Transition.java:88) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.doTransitionStep(DbmsReconciler.java:355) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.doTransitionStep(DbmsReconciler.java:356) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.doTransitionStep(DbmsReconciler.java:356) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.lambda$doTransitions$12(DbmsReconciler.java:324) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.namedJob(DbmsReconciler.java:335) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.doTransitions(DbmsReconciler.java:325) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at com.neo4j.dbms.DbmsReconciler.lambda$doTransitions$10(DbmsReconciler.java:310) ~[neo4j-dbms-enterprise-4.2.6.jar:4.2.6]
at java.util.concurrent.CompletableFuture$AsyncSupply.run(CompletableFuture.java:1700) [?:?]
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:515) [?:?]
at java.util.concurrent.FutureTask.run(FutureTask.java:264) [?:?]
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1128) [?:?]
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:628) [?:?]
at java.lang.Thread.run(Thread.java:834) [?:?]