The problem with font-size in quirks mode is that when using medium, large, x-large etc, the browser is always showing the font as one step larger than in standards mode.
This means large in quirks mode is the same as x-large in standards mode.
Try changing your code to this:
<html>
<head>
<title>IE 8 Quirks Font Size</title>
<style type="text/css">
#testDiv
{
font-size: x-large;
}
</style>
</head>
<body>
<div id="testDiv">Here is some text</div>
<div>And some unstyled text</div>
</body>
</html>
That should give you the same result in IE 8 Standards Mode as your current CSS does in Quirks Mode.
You can read about it here: http://msdn.microsoft.com/en-us/library/bb250395(VS.85).aspx
Keyword Values of the Font-size Property
The medium value of the font-size property matches the default normal font size.
The keyword values of this property include xx-small, x-small, small, medium, large, x-large, and xx-large. With earlier versions of Internet Explorer, these values are not defined intuitively. The medium value is not the default normal font size; small is the default.