Which Mobile app development tool?

I don't know if it's ready yet, but at some point Dreamweaver may be able to export via PhoneGap, so you could make mobile app versions of web pages. Other than that it doesn't apply to publishing to mobile.

If you publish AIR for iOS or AIR for Android apps you have a choice of what tools to use. Flash Pro is a highly graphical environment, where you might well lay out your interface visually on a timeline, and then have ActionScript code to make it all work as an app. The advantage there is that you can use images and animation rather than just code to do many of the effects you'll need.

An alternative to Flash Pro is Flash Builder. You can create an ActionScript Mobile project, and most likely would create most of the experience using code and external graphics that get embedded, or using a library of graphics that you created in Flash Pro.

There is another kind of project you can make with Flash Builder, a Flex Mobile project. In those you're more likely to be using an XML like layout language to place components, but also big chunks of ActionScript.

So, if you are more visually oriented, and intimidated by complex coding IDEs, Flash Pro would be a good choice. If you are more of a hard core coder, and laugh at people who enjoy graphically rich interfaces, then Flash Builder would be a good choice.