I think it's better to use a username / password simply because I don't want the user to start my IIS server to access a large number of databases. I would prefer it to be focused where, for this application there is a user, and this user has access only to this database.
You need to be sure that your web.config file is safe, so you need security.
If you want more security, you can simply use the dependency injection infrastructure and enter a compiled class with username / password and just use this connection string. This class can be confusing if you need some semblance of greater security.
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