Javascript frameworks like MooTools and jQuery are used on most modern websites. CSS selector engines are one of the most useful and widely used features in these frameworks. Because of this, selector performance is extremely important for modern web applications.
Both MooTools and jQuery have built their own stand alone selector engines for use in their respective projects. MooTools uses the Slick selector engine and jQuery uses the Sizzle selector engine.
Surprisingly, there are very few performance comparisons out there for these two engines. Below are the results of a selector engine performance test between MooTools 1.3.2 and jQuery 1.6.2. The original code for this test came from this post and you can check out the source code on jsFiddle.
jQuery seems faster than MooTools for almost any type of selector. The one big exception is the ".note" selector, which also happens to be one of the most commonly used. Given that, the overall performance of a webapp between these two frameworks is somewhat up in the air.