I'm only slightly familiar with the features of Data Tier Applications and what Database Projects did in the Database Edition of visual studio.
Are these two different overlapping solutions for database version control? Or does Data Tier Application functionality replace outright the need to use visual studio database edition and database projects?
Right now the difference between Database Projects and Data Tier Projects is at the point of deployment. If you want to create a dacpac, you'd use the Data Tier Project. If you want to createa .dbschema and sql migration file, you'd use the conventional Database Project.
As far as I'm aware, Data Tier Applications are expected to be important in future for SQL Azure deployment.
Unless you're specifically looking at SQL Azure, I'd use Database Projects for now. It all depends on what you're trying to achieve. It could be that SQL Source Control (by Red Gate, the company I work for) is more suited to your needs.