I ran a system with the best part of a thousand databases, spread across multiple servers. They were all an identical structure and were synchronised with a template database which was on each of the machines.
This allowed me the ability to migrate databases from one db to another if one was getting excessively over-loaded, and as the client mix changed, I could create new databases on different servers to load balance across the servers. This was the biggest advantage I got from the system, in that I had multiple large lumps of tin performing multiple complicated queries simultaneously on the separate servers.
The great thing about this, is that you can add servers to the configuration at your own speed, as each server starts to get over-loaded, add another into the mix, migrate some dbs across to the new server and end up with a nicely load balanced set of servers. A really nice and simple way to add scale to the system as and when it is required!
The reason I went with this approach rather than the single huge database approach, was the sheer size of the potential database that would have been created... each of the 1000 databases had 200 tables, and many of the individual tables within each of the databases comprised many hundreds of millions of rows of data!
A single database configuration would have required certain tables (approx 8 of them) to have multi-billions of rows of data, and the total db size would have been over 10Tb. We were able to have multiple servers with 5Tb of RAID 10 storage, with many databases on each.
That's what I would do! Hope it helps your decision making... :)