When to use IComparable<T> Vs. IComparer<T>

Well they are not quite the same thing as IComparer<T> is implemented on a type that is capable of comparing two different objects while IComparable<T> is implemented on types that are able to compare themselves with other instances of the same type.

I tend to use IComparable<T> for times when I need to know how another instance relates to this instance. IComparer<T> is useful for sorting collections as the IComparer<T> stands outside of the comparison.

Use IComparable<T> when the class has an intrinsic comparison.

Use IComparer<T> when you want a comparison method other than the class' intrinsic comparison, if it has one.

It depends on the entity. For example following for a class like "Student", it will make sense to have IComparable based on Name.

class Student : IComparable 
{
    public string Name { get; set; }
    public int MathScore { get; set; }
    public int EnglishScore { get; set; }

    public int TotalScore 
    {
        get
        {
            return this.MathScore + this.EnglishScore; 
        }
    }

    public int CompareTo(object obj)
    {
        return CompareTo(obj as Student);  
    }

    public int CompareTo(Student other)
    {
        if (other == null)
        {
            return 1;
        }
        return this.Name.CompareTo(other.Name);  
    }
}

But if a teacher 'A' wants to compare students based on MathScore, and teacher 'B' wants to compare students based on EnglishScore. It will be good idea to implement IComparer separately. (More like a strategy pattern)

class CompareByMathScore : IComparer<Student>
{
    public int Compare(Student x, Student y)
    {
        if (x.MathScore > y.MathScore)
          return 1;
        if (x.MathScore < y.MathScore)
          return -1;
        else
          return 0;
    }
}