Let's get the US prices straight here:
State colleges are the cheapest options. Most state have community colleges where kids spend under $10K per year, well under in many cases.
Then there are the better state U systems like SUNY in NY which cost between $20K (NY) and $30K for the UCs)California). Some states have a middle tier system like California's CSU system which is now about $20K. All of these prices include room and board.
Then there are thousands of private schools. The typical range for those is $35K to $60K per year, depending on location and quality.
The total cost for Columbia will be about $60K for the next school year, slightly more than most
other ivy league and other top colleges because of higher housing costs in NYC.
Is it worth it over studying in Argentina? IMO that depends on several things. What do you want out of life? If you want to be a global investment banker you'll need the ivy degree but a would be engineer, doctor or teacher can go anywhere and be able to get jobs in their desired fields. Though they might need additional training to work in other countries.
The second part is how much you can afford. If you can get in to a top US college and it's not a
financial strain, there are many advantages to attending one, most notably their global job networks. That degree will be recognized and respected throughout the world.
And keep in mind at the very top schools in the US over half of students get significant financial aid based on their parents' income, so if their parents make under $60K per year they attend free,and families making up to US $180K are given aid at 4 very top colleges. Other colleges give aid too as does the govt, but usually not as generous.The average financial aid package at an ivy league school is over $40K/ yr.
Take the example of an engineer. A newly minted one from UBA will find that q good starting salary is 5000 pesos. The same new engineer from an average or even less US college, let's say California State Chico, will be starting out at $55K or more. If UBA has the proper accreditation, you'll most likely have your choice of the two lives.
So you have to look at the full picture. For our kids we chose top US privates because we attended them and reaped many benefits throughout our careers.