It appears to me that if the storedVars.id variable is null, then this snippet of code will not function properly in any browser. This could be due to the fact that the condition storedVars.id != ("") evaluates to true when storedVars.id is null. It's possible that the value of storedVars.id differs between IE and Firefox or within different test environments. The underlying issue may be located elsewhere in your code. Assuming storedVars.id is not null, and all other necessary objects exist and are not null (such as selenium.browserbot.getCurrentWindow()), then this piece of code should execute successfully.
However, upon closer inspection, it seems like this code does not actually perform any actions. There are no method calls or assignments present. On a related note, many developers opt to utilize frameworks like jQuery or YUI to simplify cross-browser compatibility challenges.