TDD and Unit Testing are not alternatives to each other. In every project you should test your code, this is where you do Unit Testing and Integration and System Testing.
TDD is however, a development model. Like Waterfall and other development methods, TDD is a method too. In TDD you have some basic requirements and you write unit tests to ensure that the requirements are implemented and working. But when you are writing unit tests you realize that in order to achieve the major requirements, you need to implement more functions and classes. So unit tests in this context makes other requirements clearer.
Suppose that you need to write an application that prints the name of the computer the application is running on. First you write a unit test:
[Test]
public void ProducedMessage_IsCorrect()
{
AreEqual(BusinessLibrary.ProduceMessage(), System.Environment.MachineName);
}
and then you realize you need to implement the ProduceMessage function. You implement it as simple as it gets so that the unit test passes. You write the method like this:
public string ProduceMessage()
{
return "MyComputer";
}
Then you run the test and it passes. After that you submit your code and other members of the team gets the code. When they run the test the test fails because you hardcoded the name of your computer in the code.
So some wise member of your team changes the code to the correct form and you keep going.
It is all about choosing developers who have TDD experience. At least some of them should be experienced TDD developers I think.