this would require hand coding of the checkout form. you would need to add an onblur event to each of the billing fields to update the corresponding shipping field using javascript.
for example, the first name would use this code:
<input type="text" name="firstname" id="firstname" value="" onBlur="document.ecart_checkout_form.shipping_firstname.value=this.value"/>
select lists are a little different, for example the state list would look like this:
<select name="state_province" id="state_province" onChange="document.ecart_checkout_form.shipping_state_province.selectedIndex = this.selectedIndex">