It truly depends on the country.
United States for example greatly benefits from a certain amount of immigrants. Currently it has over 45 million.
Youth - It keeps a country young. Look at Japan for example. Japan is an extreme but white America is n't far behind. Japan's giant problem is that it's old far outweigh it's young so when it comes time to collect benefits that you worked your whole life to receive then suddenly there's an astronomical drain on the economy. US doesn't have to worry about that to spite many white Americans deciding not to have children like the Japanese, or at least not as many.
Innovation - If you go to Silicon Valley, envy of the world when it comes to innovation.. you dont have to look around for long before you see an immigrant. Microsoft's CEO is from India, born and raised. SpaceX, dude is from South Africa. Yet so many decide to pack up and move to the US permanently because immigrants thrive.
Laziness - Go to Florida for example, Orlando or Tampa.. how many people have their lawns and landscape maintained by a small family business? Not talking about rich people but rather middle class. Many. You'll see a lot of Mexicans doing the lawn service because they're willing to work in extreme sun / heat / humidity for minimum wage. If they didn't exist, something tells me it'd be far too expensive for a middle class worker to shell out $35 a week to have their lawn mowed.
Syria - The massive difference between Canada/US and Europe is much of Europe is getting absolutely everyone.. similar to Latin Americans in the US but on steroids. The major difference is the US is able to decide how much that individual or that family can benefit the US economy. They're picking out the best of the best and leaving the rest. So accepting 10,000 refugees that are completely accounted for and heavily pre-screened seems laughable compared to the 1 million immigrants in Europe, many completely unaccounted for, and some almost certainly tied to ISIS.
TL;DR: Immigrant cant actually great improve a nation, like the US. But only if you know when to open and close the valve. When you open the flood gates, you get modern day Europe. Moderation and heavy pre-screening is the key.