You are correct that if the receiving country treats holders of the respective passports entirely equally then it does not matter which one you use. Remember, for countries that do have active immigration exit controls you will need to present the passport that was used to enter the country.
One obscure but very important consideration: what happens if you get into a legal situation? Outside of immigration policy, some countries have negotiated between them agreements on how their nationals will be treated by the respective legal systems. An alien will generally* be treated by the legal system based on the passport used to enter the country. For example, many countries have agreements regarding consular access to their citizens arrested and detained by the other country - typically consular officials are allowed access within a few days of arrest, regular checkup visits, and are able to positively influence the conditions under which the person is being held.
USA and Russia are currently experiencing, um, "headwinds" in their relationship, much to the detriment of Brittney Griner. a famous US professional basketball player who was arrested and detained by Russia. Typically a consular visit is allowed within a week. Russia did not permit a consular visit by US officials for many weeks outside of the norm. In addition, consular officials are frequently able to positively influence the situation (access to legal advice or medical assistance; better food or detention facility conditions) to help the arrested individual.
So, with all other things being equal but for a variance in how a country will treat nationals of one passport over the other, that should be a factor in deciding which one to use. Of course, how a traveler can know if there is a difference is an entirely different matter - but common-sense and conventional wisdom are useful. For example, if someone traveling to Russia holds both Belarus and US passports, one could probably safely assume the Belarus passport will be more helpful than the US passport. YMMV.