What the Bulgarian and Romanian passports have in common
Both Bulgaria and Romania are part of the EU and the Schengen Area. This means that holders of either citizenship can not only move freely around the countries of the European Union and the Schengen Agreement, but also live, work, study, open bank accounts, run a business and buy property there with minimal formalities.
As for visiting other countries, both passports give the right to visa-free entry to 172 countries. The difference is minimal: Romania has visa-free access to Tanzania, whereas Bulgarians have to obtain an electronic visa there (or, alternatively, a visa on arrival). Romania previously conducted active negotiations on a visa-free regime with the USA, but after Donald Trump came to power the project was frozen, and Romanians, just like Bulgarians, still need a visa to visit the United States.
By way of comparison: Ukrainians can visit 147 countries without a visa, Russians – 125, and citizens of Belarus – 94 countries. Moreover, even with visa-free entry the 90/180 rule applies in most cases, i.e. one may stay in another country for no more than 90 days per six-month period, while permanent residence requires obtaining a long-stay visa and applying for a long-term residence permit.
Differences
It is generally held that a Romanian passport can be obtained somewhat faster than a Bulgarian one (according to reviews, the process takes on average 2 years less). In addition, obtaining Romanian citizenship involves taking an oath in the country’s official language – in Bulgaria there is no such ceremony, at least for now. There are, of course, other nuances in the procedure, but they are not very significant either.
In practice, people usually obtain the citizenship of the country where they intend to live, or whose passport they are entitled to: if you have Bulgarian roots or a record of residence in Bulgaria, it makes sense to choose the Bulgarian passport, and if you have Romanian ancestors or have naturalised in Romania – the Romanian one.