two or three things are missing in your code that you may try.
add validation group on button and validation control
add operator & type property for the compare Validator.
it will define that what datatype you want to compare and what case do you want to compare.
<asp:comparevalidator id="CompareValidator1" runat="server" enableclientscript="true" xmlns:asp="#unknown">
ControlToCompare="txthdnREsult" ControlToValidate="txtCaptcha"
ErrorMessage="Invalid Captcha Entered." Operator="Equal" Type="String" ValidationGroup="groupname"></asp:comparevalidator>