I know an estadounidense who imported a Lincoln Town Car from the States, is completely licensed and ensured to be a remis driver here in Buenos Aires, maintains the car impeccably (very difficult because they don't make parts for it here) and his door-to-door service only costs $65 dollars.
Yeah, $170 pesos or so ($45 USD) to/from the airport is a big rip off.
You can grab a remis there at the airport (if they have a ride available) for cheaper than that.
Don't go with guys who are coming up to you and asking you if you want a ride into town. Most of the time they are hustling, although sometimes there is someone actually from a cab stand that is looking to get people rides. If that's the case, they will take you to the cab stand and you will get a ticket and go in a cab, all above-board. I don't know what the official cost is nowadays for sure FROM the airport, but it's around (maybe less?) $100 pesos.
You can often get a cab here in the city to take you to the airport right off the street for the price of the meter, which is less than the "offical fare."
There is a flat rate (go to the taxi stand when you come from baggage claim). Not sure what the flat rate is now - maybe 100 pesos? Were they charging 45 for a car service? It's high but not shockingly so assuming its a nice car and driver will be there waiting. Car service is always more expensive than taxi.
After baggage claim there are several people usually yelling from taxi counters offering flat rate service.
I always use RADIO TAXI its located after baggage claim, past the people yelling... on the other side of the arrival doors you'll find their counter. They have someone to help you with your luggage too.
There is a booth right there when you exit baggage where you get a cab for 98 pesos and they will have some guy walk you to a taxi and load your bags. He is gonna want a tip, so have a couple of pesos ready. He will bitch for more but tell him tough shit.