It's clear that Mastercard-Visa is by design meant to be the other's alibi for not being declared a Monopoly.
Not the case.
Visa credit cards ($V) can be used at 44 million merchant locations in more than 200 countries and territories.
Mastercard credit cards ($MA) are accepted at 37 million merchant locations in more than 210 countries and territories.
So they're different, which doesn't matter at all except if you're stuck somewhere!
Odds are both are accepted, but it's worth checking a destination country or area within a country before traveling with just one or the other.
It might surprise that even in popular countries, V/MA might not be the most widely accepted. It's only recently that CB didn't beat both in France, though for a while CB+V was more common on a door than CB+MA, but now a CB logo usually includes both V and MA.
https://histoire.bnpparibas/en/the-carte-bleue-a-french-succ...
Also, this is a good synthesis of the duopoly* problem, perhaps less of an issue (aka lower rates) in EU likely thanks to the nationals like CB:
https://seekingalpha.com/article/4536466-visa-and-mastercard...
* About duopoly: Visa has less than a 50 percent share, MasterCard has less than 40 percent, Discover has 18 percent, and American Express has 15 percent. V and MA acting as if 90% share is most likely "conscious parallelism".
https://en.wikipedia.org/wiki/Tacit_collusion#Conscious_para...
See the duopoly example at the end of the article suggesting a multi-round (long term) Nash equilibrium for parallelism.
> As far as AmEx, might as well leave home without it.
Is referring to how American Express is not accepted in lots of parts in the world barely at all. Doesn't matter what the fee is if you cannot use the card in the first place.
I think this differs wildly between countries. I know that Discover/American Express wouldn't have close to 30% of the market share in Europe, it's only some shops that do accept those, although it's becoming more popular. In the countries I've been to in South America, things have been more or less similar.
Also, I think that link of yours (although I cannot read it fully) is about the percentage of transactions, rather than number of merchants that accept it. So it's basically more about the card holders than the merchants accepting one vs the other.
I figured it was some bug or my Visa blocking me, but a friend mentioned it to me. He had bumped into the same problem and somehow deduced that it was (likely) due to not working with Visa.