Web browsers differ significantly in what resources they make available for the running of Javascript code. Of course most of the time the resources that your javascript requires will be rather small and the code will run quickly whichever browser your visitors are using. One area where significant resources are required is with animations that use dozens (or even hundreds) of separate divs on the page to create a given effect.
My fireworks script uses one div for each spark in the fireworks display and the analog clock scripts use separate divs for each pixel in the clock hands. In each case there are a significant number of divs being moved around the page and the script performs significantly differently in different browsers. In each case after developing the script and testing in different browsers I then had to go back and adjust the scripts so that what the script was doing would not overload the resources available in some browsers.
What I found in fact is that the browsers perform similarly with the different scripts with the same browsers always being the ones to slow down their processing first. As Opera is my preferred browser for general web browsing and follows the Javascript programming standards reasonably well I usually test in that browser first. The more complex animation scripts run best in that browser because Opera seems to be able to make more resources available for running resource intensive scripts than the more popular browsers do. Internet Explorer also appeared to have no difficulty in running these same scripts (at least until I tried putting three reasonably large analog clocks on the same page). With a really resource intensive script (probably several hundred divs all moving at once) Internet Explorer ran noticably slower but not slow enough to really worry about the difference.
The problem came with testing these high resource animation scripts using the Moxilla / Netscape / Firefox family of browsers. These browsers run noticably slower with a moderately resource intensive script such as my fireworks script although not slow enough to worry about. When I tried to display my page with the three large clocks these browsers just couldn't cope. Just to be able to redisplay the clocks to reposition the second hands took several seconds and so the second hands were jumping around the clock in about 10 - 12 jumps instead of the 60 steps that they were supposed to follow. Of course I then reduced the clock sizes significantly in preparing my example page for my multi clock script so that those browsers could cope with the necessary updates to the page.Of course the addition of other Javascripts to the page (such as for displaying advertising) also require resources and this may also have an impact on the usability of animation scripts provided on your web page.
These particular scripts are perhaps somewhat unusual in that they use a huge number of separate divs to effectively draw an animated effect onto the page but they do serve to illustrate the relative resources that the different web browsers make available for scripts to use. Where you do decide to place such resource intensive scripts on your page you must remember to test them last with a Mozilla based browser (Firefox is the most popular) in order to check that the combination of scripts on your page does not exceed the small limits that this family of browsers impose. If you don't perform such last minute testing then you may render your page unusable to people using those browsers. Conversely if you enjoy viewing web pages that make use of resource intensive animation scripts then you should select a browser that is not based on Mozilla (eg. Internet Explorer or Opera) as your preferred browser as these are more likely to be able to properly display such animated effects.

