First off, in AS3 you can't put variables on an object anyway - though AS2 still has this functionality.
And look at it as you would with using functions. If you want to use a variable in every function and subfunction, declare them at the start of your frame or class. For one specific function, you should declare them inside that function, so only that function can access it - and it doesn't exist outside that function.
So, if you want to use a variable in more functions and objects on a certain frame, declare them on the frame itself. Otherwise, if it's only for that specific object, declare them on that object.