It's a good question. "deal with" is more neutral. You have an issue or problem. You must resolve it or do something about it. You "deal with" it. If you have a problem or issue which is difficult for you, then you still need to deal with it. If you are dealing with it well, despite the difficulty, you are coping with it. So "cope with" is like "manage to deal with something, despite the difficulty". e.g. I can normally cope with stressed students. I can't cope with the kids today - they are screaming too much.

You deal with some matters You cope with some issues