First of all when I say engineering, I mean non-software engineering. So think like mechanical, electronics, chemical etc.
To see how the STEM job market in Canada is behind the US and EU, you can search jobs on say LinkedIn and compare how many jobs you find in Canada that you like and say in Germany. At least in engineering, most Canadian jobs are at startups or small companies. As you'd imagine startups and small companies usually can't employ many people so there are less number of positions available at a time.
About citizens getting the jobs first, of course a much more skilled immigrant with proper English skills would take the job. But the thing is, usually whenever there's a skilled immigrant, there's also a skilled citizen wanting the job. So it's not always easy. It's usually not voiced but, assuming similar skill levels and experience, many companies will prefer employing a citizen to an immigrant. There is no law dictating that employers must prefer citizens though. That being said, if you're a very skilled immigrant with good experience and outstanding English skills, you don't have to worry about losing a job to a citizen; you'll do just fine. Also please note that, again for engineers, immigrants (and also citizens) have to obtain the license to practice engineering in Canada. Citizens of same level of experience usually already have their licenses but since an immigrant has just landed, they usually don't have the license and are at a disadvantage until they receive their license.
To wrap up; if you're an engineer, finding a job you'll like in Canada won't be very easy. Most immigrants eventually find jobs they like but the search may take up to 6 months or a year, or even more. You may even need to work "survival jobs" which are not uncommon. Canada is not a "land of opportunity" in the same meaning the US would be. It has its challenges so one must be aware. I wouldn't say immigrants face much of a discrimination in the job hunt but they sure are at a considerable disadvantage because of the nature of the things. While not necessary, getting an MEng or an MSc from a renowned Canadian university helps a lot if you focus on networking during your studies.