Well, the real difference between browsers that I care about is how well they run my app! However, I'm not sure I'm understand your point. How would those test suites help?
"... The slowdown is in the DOM ... setting the size and position of (absolute) divs, and setting their text content ..."
Run the tests (set size, position of divs, set text content) in the testing app, check the numbers returned to see how each DOM operation effects different browsers. The test app allows for DOM selection, modification or attributes for example. You can run these tests against various browsers (Firefox 2+, Safari 3+, and Opera 9+, and Internet Explorer 6+). You could use this to test which browser is slow for particular DOM operations ~ https://wiki.mozilla.org/Dromaeo#Running_the_Tests and possibly isolate where.
Of course I didn't ask if you are doing this as raw Javascript or using a library? Are you using JQuery, Prototype, DOJO?
This is where a cross-browser test suite could be handy checking which api you call against different browsers. Have you looked at http://ejohn.org/projects/dromaeo-javascript-performance-tes... then ( http://wiki.mozilla.org/Dromaeo ) and http://dromaeo.com/ to see the real difference b/w browsers?