It seems like you’re sneaking an assertion in there. Can you clarify your point a bit? What is the relationship between competition and wages, and why is one better than the other for unions?
Germany is a good example of this, they have a ton of unions and lots of production but the unions understand that competition is key to survival so there are very few strikes.
I suggest you look into the differences in the management of companies of those countries rather than the unions.
German unions also have a seat at the board. Unlike most board run companies a decision isn't made without input from the union. So yes, there few strikes in Germany because labor and management actually behave like adults.
This is why Walmart has utterly failed to expand into Germany. They thought they could take their abusive worker policies into Germany and when that didn't work they pulled out.