Generate XML document in-memory with JavaScript

The second approach seems a good way to go. It was designed to work with XML documents.
Once you have the document object created, use the standard XML DOM manipulation methods to construct the entire document.

// creates a Document object with root "<report>"
var doc = document.implementation.createDocument(null, "report", null);

// create the <submitter>, <name>, and text node
var submitterElement = doc.createElement("submitter");
var nameElement = doc.createElement("name");
var name = doc.createTextNode("John Doe");

// append nodes to parents
nameElement.appendChild(name);
submitterElement.appendChild(nameElement);

// append to document
doc.documentElement.appendChild(submitterElement);

This may seem a little verbose but is the right way to build the XML document. jQuery does not actually construct any XML document, but just relies on the innerHTML property to parse and reconstruct a DOM given an HTML string. The problem with that approach is that when tag names in your XML collide with tag names in HTML such as <table> or <option>, then the results can be unpredictable.
(EDIT: since 1.5 there’s jQuery.parseXML() which does actually construct an XML document and thus avoids these problems — for parsing only.)

To cut down on the verboseness, write a small helper library, or maybe a jQuery plugin to construct the document.

Here’s a quick and dirty solution to creating a XML document using a recursive approach.

// use this document for creating XML
var doc = document.implementation.createDocument(null, null, null);

// function that creates the XML structure
function Σ() {
    var node = doc.createElement(arguments[0]), text, child;

    for(var i = 1; i < arguments.length; i++) {
        child = arguments[i];
        if(typeof child == 'string') {
            child = doc.createTextNode(child);
        }
        node.appendChild(child);
    }

    return node;
};

// create the XML structure recursively
Σ('report',
    Σ('submitter',
        Σ('name', 'John Doe')
    ),
    Σ('students',
        Σ('student',
            Σ('name', 'Alice'),
            Σ('grade', '80')
        ),
        Σ('student',
            Σ('name', 'Bob'),
            Σ('grade', '90')
        )
    )
);

Returns:

<report>​
    <submitter>​
        <name>​John Doe​</name>​
    </submitter>​
    <students>​
        <student>​
            <name>​Alice​</name>​
            <grade>​80​</grade>​
        </student>​
        <student>​
            <name>​Bob​</name>​
            <grade>​90​</grade>​
        </student>​
    </students>​
</report>​

See example