Well Flex runs in a Flash Player in a browser, not directly in the browser so you should be able to guarentee no cross browser issues. In reality, we see the odd difference, presumably because the player for IE and FireFox (our other supported browser) are slightly different. But if you compare this to the vast differences you have to fight against using browser technologies directly (not just JS, also HTML implementation differences, CSS differences and the like) if browser compatability is your chief aim Flex is far easier.
My personal view on this issue is different, I believe if your application is small, simple and less interactive in nature then it makes more sense to implement it using JQuery, any other frameworks but you have additional overhead of testing your application on different OS/Browser combinations. For that matter choosing Flex is simple and straight solution because of its cross browsers compatibility.
However I do not think choosing Flex just for cross browser compatibility would be the right choice, again this depends on your application and the kind of problem it is going to solve. Also choosing Flex might not make sense for commercial applications in terms of licenses and costs of Flex/LCDS//Flex Builder etc.