In Buenos Aires you must try Al Galope at Tucuman 2633 for a real meat feast. Don't forget to try Kosher McDonalds in the Abasto shopping center.
In Santiago there are just a few places withing a couple blocks of each other near the Aish building- 2 are very casual and ok - Via Lactea dairy and sushi and a meat one around the corner. There is a more formal place that just opened called Mex u Yan or something like that which I think is Chinese but I didn't eat there.
Enjoy