It is quite difficult to specifically say why someone should pick one tool over another. It is much a matter of personal taste and corporate decisions.
The simple ad message is that DbVisualizer is great for developers and DBAs whereas the user need to access databases from several vendors. DbVisualizer may be used with all of them. Combine this with the fact that DbVisualizer runs on Windows, Macs and Linux/UNIX boxes. The result is that the user only need to master a single DB tool instead of at least one per database product whereas these most often only works for a single OS such as Windows.
We are not targeting DbVisualizer as for example being a TOAD replacement. However, many customers are using DbVisualizer for development activities while TOAD is used by a few number of users for heavy DBA related work. This is a quite common setup.
I'm a developer at a web shop and I can't live without DBVisualizer. Toad is a great program but you have to have a separate instance for a specific database. I like the fact that DBVisualizer allows you to connect to pretty much any database.
I believe you can connect through ODBC but we use all JDBC Type 4 drivers to connect.
On a daily basis, I connect to MySQL, DB2, Microsoft SQL Server and even H2 so I can easily create my 'create table' scripts for my unit test cases.