Kurt, you're absolutely correct about how many people in the States cook their meat. Absolutely disgraceful!
In Texas, many "immigrants" from other states continue to use propane (or charcoal), not knowing any better, but most Texans know how to slow-cook meat - particularly brisket (kind of similar to vacio, not sure the exact differences between the two cuts).
I used to slow cook a brisket in a smoker/grill (not a true smoker). It's a steel barrel cut in half length-wise and hinged (I'm sure most are familiar with the type of equipment though many may never have used one), with a firebox added to one side of the stationary bottom half of the cut barrel and a small pipe chimney on the top, hinged side - between an air gate in the firebox and a slide-able cap on the chimney you can control the temperature to within a few degrees and cook for hours, just adding fresh wood from time to time into the firebox. A good brisket may take 6-8 hours, and cooked with apple wood (not carbonized!), the light, sweet smoke that plays over the meat over that time, along with a number of different rubs or glazes or marinades, makes a barbequed meat the likes of which I rarely find anywhere else.
I don't do an Argentine-style asado, I never had anyone show me how to do it. I do, however, use the Argentine-style parilla simply because I had a house that had one, and now borrow a friend's house that has one. I've seen some barrel parillas here, but without the firebox and chimney to control heat it's just a slightly bigger "Weber" grill.
Everyone here that's suggesting you need to slow cook the meat is 100% correct. Many restaurants here don't have the time (or don't spend it) to really prepare meat correctly over a parilla. To me, even when cooked rare (I like "blue" personally) in many restaurants here, the meat can be a bit dry and/or tough and somewhat unflavored. Particularly vacio.
I do an asado (my style) most Fridays for a group of friends and acquaintances. The fire and paying attention to how much heat the meat is getting is very, very important. Also, because the Argentine parilla is not enclosed (depends - some are enclosed on 5 sides, but not all 6 ever - the front is always open), it is very important to turn the meat often (maybe every 5 or 10 minutes, depending on the size of meat, heat of fire, etc). If you don't turn often, when you look at a cross-section of the meat you tend to get dry, over-cooked meat on the outside, going more towards rare (or whatever destination you are shooting for) in the middle. Obviously, the more cooked in the middle, the outside.will be drier and more cooked if you simply leave the meat on one side, then the other, without turning it very often. When cooking ribs or sometimes tira de asado (when the meat is thick and the bones block a lot of the meat from the fire on one side, not when the whole slice of meat/bones is relatively thin) keep the time where the bones are down toward the flames about twice as long as the meat side.
I've heard so many people tell me the best way to cook meat is to cook it hard on one side for half the time (15-20 minutes with a big chunk of meat!), then turn it over and cook it hard on the other. Depends on taste, I suppose, but for me - NO WAY!. Personally, I feel like a good piece of meat should be nearly the exact same color in cross-section from the outside to the inside - but it takes repeated turning of the meat to do so when cooking over an open flame as opposed to a smoker (and with a smoker you don't tend to get things too rare anyway - but extremely juicy and tender). It takes a little longer my way, but the results speak for themselves.
As an aside, the guy who owns the house where we do our Friday asados recently bought a propane grill to put next to the Argentine-style parilla. He thought I'd prefer to use that to the parilla because it's neater (no wood/coals mess) and there's no effort starting the fire, maintaining it, etc. WRONG. Propane sucks. Go to the extra effort. Doesn't really take much... I refuse to use the propane grill for anything more than sometimes help keep some of my meat warm (far from the fire!) because the parilla I cook on is a bit small and I have to cook in shifts.
When I do our asado, I cook whole lomos, chicken brochettes with veggies and panceta stuck between the meat, salmon filets and chorizos. I've done barbeque chicken (pata muslo) and a few other things at times. I've done matambrito de cerdo (my personal favorite - particularly when the meat has a good little layer of fat on one side, not too thick - it gives a bacon-like flavor to the pork and grilled the fat is crispy and DELICIOUS!) I can't comment on cooking things like chinchulines and sweat meats because I simply don't like them and therefore don't cook them
With less-flavorful meat (like a lomo, for example), it's good to use a light marinade, about 12 hours in the fridge at least before you cook the meat. Don't use lemon juice with a lomo - it's already tender enough and doesn't give the meat a good flavor. With tougher meats like vacio, it would be a good idea to marinade in lemon water with whatever spices you might like. Ojo de bife and bife de chorizo make good meats to barbeque - being fairly tender, they have a lot more flavor than a lomo - don't particularly need to be tenderized or flavored apart from the rub you might want to put on them. The others Bajo_cero mentioned as well are good meats.
When I put a rub (chimichurri, sometimes salt and spices like cumin or maybe paprika, black pepper, etc) I like to use a little bit of olive oil coated on the meat. Cooked slowly, the olive oil doesn't "fry" the outside of the meat, but helps keep the spices attached and also helps keep the meat juices inside where they belong.
When you cook a piece of meat, cook it whole - don't get cuts (or cut them yourself) and cook them like steaks. You lose all of the juice that way and end up with a drier, less flavorful piece of meat. Get a whole chunk of meat and cut it into portions after it's cooked. After you take a meat off the grill, make sure you let it sit for 5-10 minutes off the fire before you cut it. The juices settle a little better. Also, remember the meat continues to cook a little once off the fire.
On an Argentine parilla, fire management is perhaps the most important thing. You need to keep a steady temperature to cook meat.
I have metal cylinders (bought at Easy) with handles on them and holes in the sides and bottom that allow me to build the first fire rapidly. Use leña, never briquets/charcoal. Put the leña in the cans with a fist-sized piece of cotton soaked in alcohol under the cylinder (a trick taught to me by a friend recently - much better than using wood or newspapers to get the fire started, leaves almost no residue, is hot and starts the leña rapidly. Even works if you just start a fire with a pile of leña without the cylinders - put the cotton in the center bottom of the pile). The fire I make for our asados, I use 4 cylinders of leña for the first fire.
When the leña is almost entirely white, spread the coals over the bottom of your parilla surface and make sure they are broken up into smaller, more or less equally sized pieces. Keep some of your coals to the side so that you can throw new leña on top in case you need to augment your coals as they go out. On parillas that have a grill that moves up and down, you can easily adjust the amount of heat your meat is getting. Otherwise, you have to control with the amount of coals under meat. Sometimes you need to use both methods. I usually use at least two medium-sized bags of leña for about 7 kilos of meat over an hour or so.
It takes a lot of practice to cook meat well (I don't mean well-done) on any open-coal fire. It's easy to just burn a couple of steaks (like on a Weber for example) on an open fire, but to get juicy, tender, equally cooked meat is a different story.
Not to toot my own horn, or to compare what I do too closely to Argentina asado, but you can't get meat cooked as good as I do it in restaurants in the city (at least I've never had any - maybe in very expensive places [which I don't frequent], or I just don't about some good home-style parilla somewhere). I've had some outside the city where they cook over open pits (where they stake the meat out beside the fire) and take a long time to cook the meat that and is very flavorful, tender and juicy (but not on a parilla). However, for the most part you don't end up with rare or medium-rare meats like that, but still the meat practically falls apart on your plate.
I admit it - I like blood