How to restrict user from selecting date which is already selected

You just need to change the Operator to LessThan

  Date 1<asp:TextBox ID="TextBox1" runat="server"></asp:TextBox>
        Date 2<asp:TextBox ID="TextBox2" runat="server"></asp:TextBox>
        <asp:CompareValidator ID="CompareValidator1" Operator = "LessThan" Type = "Date" ControlToValidate = "TextBox1" ControlToCompare = "TextBox2" runat="server" ErrorMessage="Date1 should be different from Date2"></asp:CompareValidator>
        <asp:Button ID="Button1" runat="server" Text="Validate" />

in the @Page set Culture = "en-GB" for dd/MM/yyyy

<%@ Page Language="C#" AutoEventWireup="true" CodeFile="CS.aspx.cs" Inherits="CS" Culture = "en-GB"  %>