Also, unity engine is written in C++ while flash use actionscript, so, performance-wise, is unity faster?
Well, the core of both unity and flash are probably both written in c++ or another more efficient language. It is your additions to the code that are going to be written in action script for flash. Unity actually gives you the option for programming in c#, javascript, or boo.
As for the speed, c# will likely be the fastest of the available languages, but I would not base my decision of the platform based on the speed of the language it uses. In my projects I have found that drawing the scene takes the most time, and that is part of the engine code already written to be fast. The code you add will probably not be the bottleneck, if it is you either have inefficient algorithms, that can be fixed, or your game is too complicated but most beginner games don't push the limits of the hardware, so you should be fine.
If your game is going to be 2D, I would recommend flash. It is much more widespread and likely an easier environment to work in. If it is going to be 3D, go with Unity.