It's a strange approach to disable a single function in another script to override it. It might be a good place to utilize polymorphism.

If the function is going to be overridden for the whole lifetime of the object it is attached to then you could just use an abstract function with two different specializations. This is how you would do it in C#

base class:

abstract class Base : MonoBehaviour { abstract protected void foo();

 // common functionality

specialization #1:

class FirstSpecialization : Base
{
    override protected void foo()
    {
        // do stuff
    }
}

specialization #2:

class SecondSpecialization : Base
{
    override protected void foo()
    {
        // do other stuff
    }
}

I haven't testet it, but I fell quite sure that C# (and the other languages can do this).

here is how C# .NET does it. http://msdn.microsoft.com/en-us/library/ebca9ah3(VS.71).aspx

Same for C# MONO, I believe.

Maybe it's too late to answer, but you can use virtual directive

Base class

public class BaseClass : Monobehavior {

     public virtual void MyFunction ()
     {
         Debug.Log("Base function run.");     
     }
 
 }

Child class

public class ChildClass : BaseClass{

     public override void MyFunction ()
     {
         // If you want to run base function as well use base
         base.MyFunction();
 
         Debug.Log("Child function run.");     
     }
 
 }

No, not in Javascript. You can't, because Javascript doesn't have classes. However, you can override functions in C#. Just declare your function as either an abstract or virtual function. With abstract in C#, you only have to declare the function in the parent class. With virtual in C#, you have to implement the method in the parent class and the child classes can optionally override that function.