Oracle SQL: How to give user the permissions to SELECT from a table

This may not be an answer but worth to check up. Some indexes may have been set to invisible as an alternative to being dropped. These are still maintained by the database but ignored by the optimizer. You'll be able to see them by querying the dictionary, but the compare tool may ignore them.

SELECT INDEX_NAME, INDEX_TYPE, VISIBILITY
FROM ALL_INDEXES
WHERE INDEX_NAME LIKE 'EMP%';

If you actually have different databases (and it sounds like you do), you can't grant permissions for users in one database to access data in another database. You'd need to create a database link in the EmployeeDB database that connects to the ContractorDB database. That database link can either use a fixed username and password in the ContractorDB database (i.e. create an EmployeeUserRemote user in ContractorDB with a password that doesn't change that can be hard-coded into the database link definition) or that database link can be a CURRENT_USER database link in which case the username and password would need to match in the two databases for every user that wants to use the database link. Queries that use the database link log in to the remote database (ContractorDB) as the specified user and have the privileges of that user in the remote database.