For your engineering degrees, you'll definitely want to have some sort of home engineering lab to apply the theory you learned to real-world applications. With an in-person university, they'll provide all the equipment you need on-site.

Is the question in relation to immigration requirements, or for job prospects? For the former, any accredited university will likely not have a problem being recognized, not unless it's a for-profit university or has a sizable "controversies" section on Wikipedia. Online degrees from an established public university generally bear the name of the university at-large, so there'd be no noticeable difference when looking at the diploma.

As for the job prospects, that's going to be very market specific. Perhaps the larger question is whether an online degree or not, is there enough demand in your prospective countries for MEs and EEs that employers are willing to go with a new resident from abroad, rather than from one of the established local universities?

I can't see how you could major in mechanical or electrical engineering online. There are projects, there are labs that you have to do, and that happens by coming in-person and working together as a team.

You'd miss out on so much by doing it online and I'm not sure how the curriculum is formatted

The reputation of the school you get your degree from will make some difference (i.e. MIT) but isn't the most important thing. If you're worried about competing with degrees from in person schools though, you may be able to find one that accepts online transfer credits and finish out your last year in person and attend the necessary labs as needed to get the degree from that school plus some hands on experience. You'll need to do some homework and confirm details with the school first.

No matter how you get the degree though, working on and documenting projects outside of any class work, especially with clubs and organizations like for robotics or racing, makes the biggest difference imo. Its the projects that demonstrate your ability to apply your skills and knowledge and solve problems and that is what interviewers and hiring managers will want to hear.

Good luck!

Edit: forgot to mention the in person classes and clubs can also help with networking and references which is often just as important as anything else.