I don't understand why you would want to copy the value of one input field to another (albeit, hidden). But if that is what you want to do, try using the below code.
The function attached to the onblur
event of the input field would set the value of the input field to the hidden field whenever it loses focus.
The window.onload = setValue
will do the same on page load.
HTML
<input id="tag1" type="text" name="tags" class="tags" value="@Model.list" onblur="setValue();" />
<input type="hidden" name="tag" value="tags" id="tag1_hidden" /> <!-- Note the addition of an id attribute -->
JavaScript
function setValue() {
document.getElementById("tag1_hidden").value = document.getElementById("tag1").value;
}
window.onload = setValue;