I don't know much about Chile in detail, I've read things here and there that talk about how relatively stable and improving is its situation.
I've lived and done business in Argentina for the last 7 years and have had occasion to pick up a thing or two about its more recent economic history, not to mention having lived some of it. However, I really don't have a ton of time to do in-depth research (though I am interested), so a lot of things that occur here I still don't have a good understand as to "why". But some things just feel "obvious" to me, doubtless because of half a century of experience about how things work in general, human tendencies we all share, etc.
No one said much about the cycles of economic problems Argentina seems to cause itself (at least I didn't see it in this thread), though someone made mention of the way governments here seem to reverse course from previous administrations and spend a great deal of time, resources and energy on undoing whatever the last administration did.
I came here in 2006 when the exchange rate was just under 3-1 peso to the dollar. I could buy groceries for a week for two of us for about $300 pesos (without buying a lot of items imported from the US or Europe - those were still a bit expensive), maybe even a little less. I remember $100 pesos buying enough that I would have to have my wife (then my girlfriend) with me to help me carry the bags. Maybe I could have handled it all, but it would have been an uncomfortable walk
The Paraguayan Guarani to the peso was around 2800-1 if I remember correctly. Maybe as high as 3200 at times.
Argentina was nearing its height of recovery after the default and subsequent crash of 2001. People were optimistic.
Now, I exchange dollars at 9-1 or better (minus the month or two where the rate dropped for a bit). But 100 pesos can buy me as little as half a small supermarket bag depending on what I'm buying (but still no "premium items").
The Guarani trades now in Paraguay for about 700-1. I mention the Guarani because I do know something about that country and its economy.
Here we are about ready to have another crash of some sort, or at least not much real growth (I think it will be a crash, but I'm not an expert). Another government will come in and (hopefully) head off in another direction to undo some of the policies that have helped exacerbate existing economic problems and have caused real problems.
I understand the argument about losing industries on opening up trade here before, and certainly that's right as far as it goes. But the real answer isn't isolating the country and forcing the market to industrialize. No nation can bootstrap themselves like that, at least not before a few decades, and even then, look at experiments like the old Soviet Union - it might work in fantasy land but it doesn't work in real life because market forces are too complex and the people that are trying to force the issue don't have a good enough understanding of basic economics many times, and complicated with corruption and nepotism, you get worse results than if you just left things alone.
To fix a country's economic issues, you should have a plan of gradual change. Coming in and suddenly opening markets when your industries are not up to par with those you are going to compete with isn't going to get you anything but problems. Reversing that suddenly and isolating yourself when you have little money and industry to start with is going to do nothing but dig the hole deeper. Argentina needs to be able to plan long term, and it is obviously too unstable politically over the term of decades to achieve that.
This is all without examining the mindset of the people in Argentina as a root cause of the instability, which is one of the "whys" I don't get yet and could have a bearing on whether Argentina has the capacity to pull itself up and stop the cycles. I'm not trying to be insulting, but it seems to me that the majority of political ideals here are one form or another of Peronism, all the rest being a mix of anything from Communism to Libertarianism (I only mention the latter because I have a friend who at one time in the States was active in Libertarian politics and is part of the [extremely small and fledgling] Libertarian party here). I don't think Peronism is a particularly efficient means of turning the country into an economic powerhouse, but that's my opinion.
However, at least Nestor's brand seemed to be a bit more stable and pragmatic than his wife Cristina's. And I think that's important.
At the end of the day, there are many political forms, and they all work to a greater or lesser degree until they collapse and something else takes its place. One of the biggest requirements, I believe, to have even a low-performing system that works somewhat and at least produces some growth over the long term and doesn't collapse, is stability and a plan that is more or less followed from one administration to the next.
The question may be "who currently has the best economy" and maybe that is a little hard to declare 100%. But it seems obvious to me, based on what I've read and heard as far Chile goes, and based on the same type of information, plus what I've lived, here in Argentina, I think Chile is set to outperform Argentina in most every respect, in the decades to come. As long as things remain stable in Chile and unstable in Argentina.