This is a good and difficult question. For both models there are pros and cons. The main advantage of one large database is that you can easily analyze (search, display, etc.) for all users. The main advantage of one-db-per-user is that each user has their own sandboxes, which can be pleasant for your SLA. In addition, this means that the amount of data in each user database can be relatively small.
If you can provide more detailed information about the stored data, relational modeling and the queries that you hope to do, I can probably give you a more satisfactory answer.
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