Solution 1:

To answer your question:

.html() will just call .innerHTML after doing some checks for nodeTypes and stuff. It also uses a try/catch block where it tries to use innerHTML first and if that fails, it'll fallback gracefully to jQuery's .empty() + append()

Solution 2:

Specifically regarding "Can I rely completely upon jquery html() method that it'll perform like innerHTML" my answer is NO!

Run this in internet explorer 7 or 8 and you'll see.

jQuery produces bad HTML when setting HTML containing a <FORM> tag nested within a <P> tag where the beginning of the string is a newline!

There are several test cases here and the comments when run should be self explanatory enough. This is quite obscure, but not understanding what's going on is a little disconcerting. I'm going to file a bug report.

<html>

    <head>
        <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.4/jquery.min.js"></script>   

        <script>
            $(function() {

                // the following two blocks of HTML are identical except the P tag is outside the form in the first case
                var html1 = "<p><form id='form1'><input type='text' name='field1' value='111' /><div class='foo' /><input type='text' name='field2' value='222' /></form></p>";
                var html2 = "<form id='form1'><p><input type='text' name='field1' value='111' /><div class='foo' /><input type='text' name='field2' value='222' /></p></form>";

                // <FORM> tag nested within <P>
                RunTest("<FORM> tag nested within <P> tag", html1);                 // succeeds in Internet Explorer    
                RunTest("<FORM> tag nested within <P> tag with leading newline", "\n" + html1);     // fails with added new line in Internet Explorer


                // <P> tag nested within <HTML>
                RunTest("<P> tag nested within <FORM> tag", html2);                 // succeeds in Internet Explorer
                RunTest("<P> tag nested within <FORM> tag with leading newline", "\n" + html2);     // succeeds in Internet Explorer even with \n

            });

            function RunTest(testName, html) {

                // run with jQuery
                $("#placeholder").html(html);
                var jqueryDOM = $('#placeholder').html();
                var jqueryFormSerialize = $("#placeholder form").serialize();

                // run with innerHTML
                $("#placeholder")[0].innerHTML = html;

                var innerHTMLDOM = $('#placeholder').html();
                var innerHTMLFormSerialize = $("#placeholder form").serialize();

                var expectedSerializedValue = "field1=111&field2=222";

                alert(  'TEST NAME: ' + testName + '\n\n' +
                    'The HTML :\n"' + html + '"\n\n' +
                    'looks like this in the DOM when assigned with jQuery.html() :\n"' + jqueryDOM + '"\n\n' +
                    'and looks like this in the DOM when assigned with innerHTML :\n"' + innerHTMLDOM + '"\n\n' +

                    'We expect the form to serialize with jQuery.serialize() to be "' + expectedSerializedValue + '"\n\n' +

                    'When using jQuery to initially set the DOM the serialized value is :\n"' + jqueryFormSerialize + '\n' +
                    'When using innerHTML to initially set the DOM the serialized value is :\n"' + innerHTMLFormSerialize + '\n\n' +

                    'jQuery test : ' + (jqueryFormSerialize == expectedSerializedValue ? "SUCCEEDED" : "FAILED") + '\n' +
                    'InnerHTML test : ' + (innerHTMLFormSerialize == expectedSerializedValue ? "SUCCEEDED" : "FAILED") 

                    );
            }

        </script>
    </head>

    <div id="placeholder">
        This is #placeholder text will 
    </div>

</html>