Private to Public Procurement

I have to decide between staying at my current company or changing the job, country, industry and procurement method.

About me: Male , late 30s , not married, no kids Sector: Automotive Industry; Location: Brussels; Field: Procurement; Salary: 3200 net/month;
Company Car: Yes; Contract: Permanent

Job Offer: NATO; Location: Luxembourg; Field: Public Procurement (they offer a lower position); Salary: 6500 euro net/month; Company Car: No; Fixed Contract: 3 years;

Disadvantage of living in Luxembourg: very high rental prices (e.g 2k euro basic rent/month for 1 bedroom apartment without charges), purchasing power around +65% more expensive versus Brussels.

What would be your advice?

Thanks for the feedback!