My friend is Vietnamese. Even though she's fairly wealthy, owns two houses and has her own business, she's been turned down for a European tourist visa twice, presumably because she applied at a single female and they don't want sex workers. Each application costs her a few hundred dollars. It's not just a matter of applying for a visa.
Meanwhile, I have an EU passport. I've traveled to around 30 countries. The only time I was even briefly questioned by immigration was coming in to Australia. Every other time it was just an immediate stamp and wave through.