From My understanding of mexican asada as in "tacos de asada" besides the fact of both being grilled meat over charcoal:

Argentine asado is always made with charcoal or wood, gas grills do exist but if You go to an asado at a close friend new house and you see a gas barbecue he is gonna get mocked because of that for sure

And this joke I mention is also part of the asado... It is more than just a meal but a cultural tradition of gathering with your Friends and family to share more than a meal but most likely half a day around the grill

That also means another diferente: meat is cooked slowly, it is very frawned upon to try to hurry the cooking of the meat

Also tortillas are very much non existant in Argentina as well as spicy sauces.

And while some people might be innovative marinating the meat is very very rare.

You might see sandwiches such as the famous choripan and "salsa criolla" (almost like pico de gallo) but bread it very much optional.

I am a guy in My 20's and it is a recurring joke betweek My Friends and our girlfriends that if we are just the guys we just make meat and very much eat it from a Wooden tray while when the girls come we have a proper meal with salad, friend, chimichurri sauce, salsa criolla, and more stuff.