I reckon Salesforce 2 Salesforce cannot be enabled for two orgs within the same salesforce organisation (I.e. two sandboxes under the same production org)
It can only be enabled across two different (partner) orgs, I believe even across two Developer orgs would work.
Besides, a full copy sandbox and a config sandbox will have significant differences in data storage limit.
I've seen a tool like Monarch from Dreamfactory used to seamlessly move data between sandboxes.
The other alternative will be using the Apex DataLoader to move and externalId fields to join up records.