I know that all the cool animations are created in Flash (the program) unfortunately, I am not very good with it. However I like flash builder, because you can use a markup language and because it is better optimized for large projects.
Can you create animations that are as good in flash builder?
It depends on what you mean by "as good."
Certain animations, like transitions and object movement (tree node opening/closing, etc.), can be very sophisticated and are actually easier to do programatically.
For other effects, like football players running across the screen, you are probably not going to be able to do them well, if at all, in FB.
Flash Builder and Flash each have their appropriate uses. While you technically can make good applications with Flash and good animations with Flash Builder, it's much harder than using the appropriate tool for the job.
If all you want to do is programmatically move some sprites around the screen, Flash Builder will work fine. If you want more complex stuff that you want to build visually, it will be easier and better with Flash.
Take a look at one of the more popular tweening engines, TweenLite: http://www.greensock.com/tweenlite/
It can create pretty complex animations purely in code, however for things like character animation there's nothing beats the good old timeline + a bit of onion skinning.