I doubt most people who are living here sans car have actually "seen all sides" of BA. To see how most of the city is living you need to travel to the outer barrios. Or go outside of Capital and see the "real" Argentina -- on the highway out to Hurlingham you'll see some lovely views -- miles and miles and miles of Villas. Electricity and perhaps water in some of the houses, but no ABL services... so the rubbish gets dumped right beside, and then the rot and waste leaks out into the streams and marshes surrounding where little kids are playing. Beautiful, really.
Lee, if you want to help, don't give money - give time, give food, or give money to reputable organizations (HelpArgentina is an American-run charity, UNICEF is active here, and there's a whole roster of others).
Most of those kids begging in Palermo / Las Canitas are forced to work by gangs -- older boys that force them to go beg.
When the girl said "now I can go home and sleep" more than likely she did not mean she was bringing that home to mum and dad. She's got to go pay it off to some older kid and get her 5 pesos or whatever they'll give her.
When you see a cute little kid that's hard to turn down. But if it were the 15 year old a**hole that's ordering her about you probably wouldn't think twice about keeping your money. It's a crap situation and as sad and mean as it sounds not to give money, by giving money you're just encouraging the situation. I know it's irrealistic to ask everyone to stop giving money, but it's just contributing to the problem. Give your money to schools, to children's organizations, to women's shelters.
I'm not saying I've got the answer but I really don't think it's giving money to these kids -- give them some food, buy them a gaseosa, do something other than throw your pesos around (oh and, by the way -- giving 100 pesos away on the street, probably not the smartest thing -- it's a great way to find yourself getting mugged a few blocks down the street).
The other thing you can do is micro-lending. Right now there aren't a lot of projects in South America available as Bill Clinton has been doing a lot of rounds promoting this site, but they are meant to be adding more. If you want to truly make a difference and don't want to go the traditional-charity route, this is a great way to do so:
http://kiva.org/