If you need to secure and audit access to the production database then Windows Authentication is a better choice than Sql Authentication for a number of reasons:
You can control exactly who can access the database via NT groups and permissions, which means you know who specifically has access to the database. The pool of access with sql authentication is only limited by who knows the password. Given n people who know the password, tracking who did what at a certain point of time is trickier (but not impossible) given that.
Only your sysadmins need know the password for the nt identity with access to the database; in fact, much of the config can be done only knowing the username
Logins and access can be tracked at the domain level far more easily than with SQL Server logins.
What it wont give you is:
Ability to ensure that the developers can't see production data - whoever writes the app can easily include some diagnostic routines to select out data
Ensure that production data only stays in production - anyone making a backup of the production database (say to restore it to a UAT environment for testing) could easily expose production data.
Problems with this approach have already been discussed in other posts; in particular, with ASP.Net applications, you have to consider whether or not you are going to use Impersonation/Delegation (webserver can act as the NT user accessing it) or a Trusted User model (where you configure a fixed identity to access certain resources).
This is further complicated by the IIS version you are using.