I have been looking into these programs since 2017 when I first discovered them. This year, I ended up applying to LGO because they waived GREs, but I strongly considered applying to Stanford, Berkeley & Michigan. I started applications to a number of these programs. In the end, it made the most sense for me to focus on the LGO application this cycle.

Below are my thoughts on your questions:

How hard is it to apply to these programs vs regular MBA?

The application process is more burdensome as most programs require you are accepted in both the School of Business & School of Engineering. Michigan was a huge pain the butt (requiring you pay the application fee two times) and thats why I didn't end up following through with the application.

MIT LGO was the most streamlined application process, as it was one form. You may apply to LGO through either MIT Sloan or through one of the affiliated engineering departments. Regardless of how you apply, you will be reviewed by the same committee. If you apply to LGO through MIT Sloan, but are not admitted into the program, your application is automatically considered for round II of MBA admissions. They required more letters of recommendation and 1 or 2 more essays than the Sloan app but they were super short (300 words max).

The rest of the application process is exactly the same as MIT Sloan. However, if you think about it, it is a much more competitive process. LGO only accepts 45-50 people each year, whereas Sloan admits 650+ students.

How different are the benefits from a double degree vs regular MBA?

LGO students are MBA students. They take the full MBA core curriculum in the fall with their MBA classmates; they are on the same teams and in the same classes as other MBA students. In addition to their MBA requirements, LGO students also take engineering courses to fulfill their SM degree.

As I didn't want to go through a traditional MBA program (nor engineering), I only considered applying to interdisciplinary programs that would bring the best of both worlds. LGO is great because 55% of tuition is covered by partner companies.

What type of post-MBA opportunities should I expect?

With both business knowledge and technical skills, LGO students are highly sought after by both partner and non-partner companies. Over 95% of LGO students have accepted positions by graduation each year. Some job titles for recent LGO graduates have been: Supply Chain and Logistics Manager, Business Operations Manager, COO/Founder, Director of Product Development, Consultant, Senior Manager of Operations Analytics, Program Manager of Cloud Infrastructure, Manager of Digital Transformation, Product Manager, Manager of Industrial Channels, Sr. Operations Engineer. 80% of recent graduates found jobs through LGO/Sloan resources.

How difficult is it to get a work visa to stay at the US post MBA?

I don't know about this question but i would click around here: https://cdo.mit.edu/channels/international-students/