Since you are using Master and Content Pages the ID of the TextBox changes and hence the following won't work as it is not able to find the TextBox.
<asp:TextBox runat="server" TextMode="Password" ID="txtConfmPasswd" MaxLength="20" CssClass="validate[required,equals[txtPasswd]]"></asp:TextBox>
Thus the only way to solve this issue is setting the CssClass from code behind so that we can pass the ClientID of the other TextBox
txtConfmPasswd.CssClass = "validate[required,equals[" + txtPasswd.ClientID + "]]";