From a conceptual standpoint just remember there are three types of cleaning/blasting results: open, closed and neutral. If a part is really bad you usually have to use something like sand blasting or similar. This leaves an 'open' structure, ie the microscopic pores in the casting are opened up. This has two problems, it makes it much more susceptible to new oxidation and holding onto grime. Using bead, either glass. metal or whatever beats down and 'closes' those pores which leads to a better looking and more durable finish. Of course some kinds of cleaning don't directly affect the pore structure and so are neutral.
As to soda blasting, etc, I don't know enough about it to know if it opens, closes or is neutral. Perhaps someone here can say.
So you use whatever is appropriate to get it clean but then if it is a process that opens the casting you need to follow with a closer.
On a practical level, I use a well worn stainless steel brush just for this purpose. When there's nothing else to do, I just pull up a chair, turn on some tunes and lightly, repeatedly start brushing.