There's no difference between hubiera and hubiese. You can use it interchangeably. It means exactly the same thing. The reason? I have no idea.

I learnt that both options are correct and they mean the same too. So in my opinion there are no difference between them. I didn't hear about any particular use as Eric says, but I'm not a teacher.

@Eric I never thought about that before, is that a rule? The first I heard of it.

There is a case when you can not use -se. “Si me lo hubieses dicho antes, yo lo hubiera hecho.” My understanding is you can’t use the -se ending in the independent clause there.

Como si fueras rico / Como si fueses rico - They both mean the same thing, but one tends to be more formal than the other. (Fueses) tends to be more formal.