It's very dependent on where you are. I'm from Europe and here it's extremely competitive. In some developing countries though, it's less competitive because there is a great need for university-level teachers, but research is far from the priority in these jobs (according to some of my friends who took them). It all depends on what you're looking for. If you want a research-intensive job in a developed country, expect as much competition as you would in the US: you're not the first one who has the idea to move to get a job.
But are all university-level math jobs posted on mathjobs.org
No. Outside the US, posting job ads on mathjobs.org is the exception rather than the rule.