I love picanha, a Brazilian cut, but I'd be surprised if Argentina didn't have an equivalent.
I'd say there's a pretty hefty difference with the idea of smoke in south american cooking. All the grilling I've read about or witnessed was direct, open fire grilling, traditionally over wood. Not the enclosed, indirect, low temp N. American smoking method. You will get a unique flavor from high heat grilling over wood (its the only time I really like using mesquite, which can be a bit like a cigarette butt as a low temp smoking wood, but makes a fantastic cooking fuel for direct grilling). I love a good steak over a blazing wood fire.