There is also a third option, which is to send them somewhere else. There are a number of countries in Africa that are poor, but still aren't in the midst of any active war or genocide. If you're from a country that is, why not go there?
The answer is that the real reason so many want to come to the EU isn't the humanitarian crisis at home, it's for the better money. But when that's their primary motivation, and they have the same alternative as anyone from any of the other countries they could live in, then their claim is no better than anyone else's.
It's fair to not want to be in Libya right now, but when you have the option to move east, west or south, there is a lot less moral force in the argument that you have a right to move north.