I've been told several times or I've read in various places (can't remember where exactly right now) not to use Tween classes from the Flex SDK but to use instead other animation libraries like Tweener, TweenMax, GTween, ...
What's wrong with using Flex tweens? Is it a performance issue?
If I want to do states transitions, should I make custom transitions with third-party libs?
Depending on what blogs you've been reading they might have an emphises on flash/actionscript. In which case it might recommend something like tweenlight or similar.
If you are using flex and its libraries then there is no reason not to use the flex effects (which are based on flex's version of Tween). Note that the flex Tween is different than the flash Tween. But you don't really have to worry about that, if you wish to move something, just use the Move effect, if you wish to fade something then just use the Fade effect.
Some people may recommend another tween package because it makes the overall SWF size smaller, but it depends on how you are building the end SWF. Are you deploying the SWF with the flex framework as an RSL (recommended although Google can't search your SWF yet if you do this, check this link) then it would be best to use the Flex effects. If you're not using the framework as an RSL then it would be a case of test you app to see what version came out as the bigger SWF file.
I've never had any issues with performance using the flex effects. Some of the 3rd party tweening packages do effects that are not part of the flex library, but other than that I can't think of any good reason not to use the flex effects/tweens.
For reference, here are some helpful things:
If your goal is just to do state transitions in skins, then it is easiest to use the Flex Effect classes. Flex 4 is about to be released and it has completely rewritten its Effect library, much faster than Flex 2/3. I ran a quick test with tweening 100 mx.controls.Button instances 500ms each, one after the next, using TweenMax and Flex Effects, and TweenMax was about twice as fast (meaning I could see 15 objects moving at once instead of 7 or 8). So if you can, I would do all animations with TweenMax. Definitely the most versatile/popular/modular/optimized. But for skins, and because Flex Effects are ready to use in skins in MXML, use them.
Also check out Tink's Efflex Flex Effect Library for some nice Container/Viewstack effects (some in 3D).