The people in countries in the European Union (and a few others in Western Europe) are really good at creating societies that are pretty nice to live in, all things considered. Different countries are nice in different ways and there tend to be trade offs with some being nice because of climate and relaxed lifestyle and others are nice because of greater orderliness or prosperity. These are trade offs (what place has governments and cuisine that are equally appealing?) and no one place has it all but even the worst places in the EU are still pretty good places to live.
The people in Africa and the Middle East aren’t so good at creating and maintaining societies that are nice to live in and even in more peaceful times and even when the economy is going (relatively) better lots of people remain dissatisfied and want more. There reasons for this are complicated involving cultural and historical factors and not all of it is their fault (yes colonialism and incessant meddling by outsiders both plays roles in this). And of course US military policy under the rule of the Neocons (aka the worst people ever) have made things a lot worse in some places… but the people in these countries are still more than capable of messing things up on their own and they tend to do so with distressing regularity.
The result is that far more people would like to move to Europe than Europe could ever allow in. And European countries together (as in the EU) are terrible about dealing with problems that individual countries could manage if left to their own devices.
The EU is slow and reactive and terrible at coming up with policy and by the time a policy is agreed upon it’s no longer relevant. As the populations in the Middle East and Africa continue to swell more wars will break out and unrest will continue and more and more people will think about how much nicer things are in Europe than at home and greater European integration will mean greater European sluggishness and fecklessness in dealing with the problem.