on Windows
Firefox 1.5
A fresh install. No extensions. 396KB, 1000×1224.

Firefox 2.x
A fresh install. No extensions. 400KB, 1000×1240.

A bunch of extensions: ~25. 399KB, 1000×1235

IE 5.0
MultipleIE install. 156KB, 1000×679.

IE 5.5
MultipleIE install. 530KB, 1000×1452.

IE 6.0
MultipleIE install. 404KB, 1000×1221.

IE 7.0
Default install. 384KB, 1000×1221.

Opera 9.1
Default install. 392KB, 1000×1261.

Opera 9.2
Default install. 399KB, 1000×1242.

Safari 3 beta
Default install. 484KB, 1000×1132.

Observations on Windows
All libraries behave equally fast/slow on the different Firefox installations. Except jQuery and mootools on my default FF install. This could be caused by GMail Notifier, which is checking my mail every minute.
IE7 improves speed by factor 2. Frustrating is that IE5.5, IE6 and even IE7 return different results on the * selector compared to other browsers and compared between the libraries.
Opera 9.2 is slower than 9.1.
Safari is in beta and is a freshman among Windows browser, so results are “just for fun”.
Prototype, mootools and dojo are the winners. I am somehow disappointed by jQuery.
on Linux (ubuntu feisty)
Firefox 2.x
A fresh install. No extensions. 375KB, 1000×1190.

A bunch of extensions: ~25. 375KB, 1000×1190.

Opera 9.2
Default install. 325KB, 1000×1192.

Observations on Linux
Opera is the faster one on my Linux box, but it took an awful long time to load the official test page.
Both Firefox 2.x profiles, clean one and one with a bunch of extension, behave quite equally - there are no speed improvements by factor 3 like mootools on Windows.
I couldn’t find any trident or WebKit browsers for ubuntu, but if you know of any feel free to drop me a line and I will run test once again.
We have the same winners - prototype, mootools and dojo.
Final Notes
Observations
Overall: libraries are running faster under Windows.
Locally I’ve tested also MochiKit - it threw a lot of errors.
Download the Shots (CC BY-SA)
Download SlickSpeed on Windows & Linux (~4.8MB).
Update: Note, that the Konquerer screenshot is not included in the archive. Download it separately.