Considering it’s only a few hours drive between the attractions on either side of the border, there’s no reason why you can’t explore both. You can easily fly into Comandante Armando Tola International Airport near El Calafate in Argentina and fly out of Presidente Carlos Ibáñez del Campo International Airport near Punta Arenas in Chile, or visa versa. However, if you have hired a car as your means of transportation, you will need to return it to the country you rented it in before departure.