I'm a bit confused with the purpose of these programs.
For example if I want to create a game or utility app that runs on air. Can I design it in Flash Professional and later open in Builder for more heavy coding? Or is Catalyst supposed to be used as the design program?
I used to think that you design stuff in Flash Professional and then open the project up in Builder to do more deep coding.
Though all the three can be used for most of the purposes u have mentioned
Flash Catalyst is more of a product used for creation of rich interactive interfaces
Flash Pro is more used for creation of rich interactive and immersive applications and RIAs(ex games,websites etc- design oriented apps)
Flash Builder is more suited to building business apps and RIAs which includes support for intelligent coding, debugging, and visual design and features powerful testing tools.(coding oriented apps)
+ all the apps can be used across multiple platforms
Hopefully this was helpful