It can be done very easily. In your code your dates are actually strings, so all you have to do is to convert them to date:
Code:
Dim a
Dim b 

a= "05/23/1999" 
b= "01/23/2000" 

If CDate(a) > CDate(b) Then 
    Response.Write "a is greater than b" 
Elseif CDate(a) = CDate(b) then 
    Response.Write "a is equal to b" 
Else 
    Response.Write "a is less than b" 
End If