I use two tests: The SunSpider benchmark from the WebKit project, and the V8 benchmark suite from Google, both of which run a variety of computing tasks rather than real-world applications. Such synthetic benchmarks are always tricky business, often not aging well as technology improves, but these two are widely used.
The upshot: Chrome wins both tests handily, with Firefox in second place on Sunspider and Safari in second place on the V8 benchmark.
I'm using raw versions of these browsers, though. Chrome is available in three versions, stable, beta, and developer preview, and I'm using the latter, which is the least stable. The latest Chrome developer preview, 220.127.116.11, includes a.
Also in my tests are Safari version 3.2.2 and the beta of 4.0, Mozilla Firefox 3.1 beta 2, Microsoft's Internet Explorer 8 release candidate, and Opera's version 10 alpha.
The Safari 4 beta had a respectable showing on version 3 of Google's tests, for which a larger number is better. Its score of 1,396 meant it's the first browser to come anywhere near Chrome, which this time around achieved a score of 2,240. Opera scored 202, Firefox 181, Safari 3.2.2 173, and IE a pathetic 63.
On SunSpider 0.9, the results were a more even distribution. Chrome scored 1,775--and bear in mind that here smaller numbers are better--to Firefox's 2,671, Safari 4's 4,257, Opera's 5,513, Safari 3.2.2's 6,345, and IE's comparatively feeble 7,168.