Just came back from Argentina. Thought I'd post my feedback since I was looking for this information six months ago.
I was not able to use the Uber app anywhere else except for EZE in Buenos Aires, but upthread posts has workarounds apparently. Upon exiting EZE, I saw clusters of police gathering at the curb. Since Uber isn't exactly legal in Argentina, I didn't want to risk it, so I went back inside to get a cab at Taxi Ezezia booth instead. I was charged 780 ARS pesos cash to go to San Telmo last month, but IIRC this is a flat fee. If you were to pay by credit card, I think the charge would have been 830 ARS. There's ATM machines near the Taxi Ezezia stand if you don't have ARS cash on you. My Spanish is terrible at best, so it was a relief that the people who work at the Taxi Ezezia booth speak English. Know that there will be a baggage handler who will help you with your luggage and direct you to the cab you will be in. He will ask you for a tip, so have some small change handy.
This is what the Taxi Ezezia booth looks like:
https://www.buenostours.com/wp-conte...taxiezeiza.jpg
I hope this helps someone.
As for Cabify, I had tried to use it in Buenos Aires (looking to go from where all the theaters are to San Telmo). It took several minutes (think closer to 10 min) to find a match, and each time a match was found, the cab driver would cancel the ride. I ended up just hailing a cab from the street. So, my experience with Cabify wasn't exactly stellar. That said, my friends who live in Buenos Aires swear by it, so I guess if a match was found, it is fairly reliable.