Seems like Chimichurri is somewhat like a Garam Masala, in that the ingredients can vary by family, region, availability of ingredients. I'd say find one that best suits your palate by refining it.
The advice I will give is to use flat leaf (Italian) parsley over the curly Domestic kind. Also, if you do use parsley or basil, blanch and shock the leaves so that your sauce retains a nice lively green shade, as opposed to a dull dark green.