Firstly, I need to give you a few basic explanation on how frequent flyer programs (FFP) work so you have a clearer understanding before you decide on which program to credit your points to.
A common misconception people have is FFP points are transferable between programs. No, in most cases, even amongst partners, you can’t transfer points. Eventhough Krisflyer (KF) and Avianca’s Lifemiles (LM) both belong to Star Alliance, you can’t transfer between the 2 FFPs. Only a few exceptions in the world such as KF and velocity, or BA and Iberia’s Avios. But generally, the answer is no.
But that doesn’t mean you can’t redeem partners award. So if you want to redeem Avianca flights, you can use KF points to redeem it. But you don’t redeem with Avianca but you redeem with Singapore Airlines. So you need to contact KF and Singapore will be the airline that issues the ticket on an Avianca operated flight.
Or, alternatively, you can credit your Singapore airline flight (if that’s the one you fly to South America) to LM. So when you book the flight, you simply put down your LM number, then you can use the LM points to redeem Avianca flight or any other star alliance flights including Lufthansa, ANA, Asiana, Swiss…etc.
Likewise, if you fly LAN or Qantas, you can credit the points to either program and redeem flights on either airlines or any other Oneworld partners (including Cathay, BA, AA, JAL…etc).
On with these basic understanding, you need to ask yourself, which airlines and what route are you most likely to redeem your points on. It doesn’t have to be restricted to South America. I have millions of points with LM yet I have never flown Avianca (I haven’t even seen one in real life!) and have been to South America for a week only in my entire life! So knowing which route and airlines that suits you most, then you can decide on which FFP to credit your points in. Each FFP has it’s pros and cons and I advise you to read the guides section in Keith’s blog to see which one suits you best. Everyone’s need is different, and I can’t really tell you which one to use. If your need is simply flying in South America, then any Star Alliance or Oneworld airline’s FFP can do that. But each one suits different needs (eg. If you are looking at short hops <1000 miles, BA’s executive club is the best. But if you are looking at one end of South America to another, then a zone based program such as KF may be more suitable.)
With regards to which program is easier to accumulate points, again it depends how you plan to accumulate. KF can be easily earned using many credit cards in Australia. This can be very useful to top up points. Alternatively, if you credit your points to LM, it is very easy to purchase miles from LM. If you want a program that is affiliated with LAN and is easy to earn in Australia, you can’t go wrong with Qantas.
Sorry I mightn’t have answered your question yet. But with a few basic understanding, I hope this will help you decide which is the best to choose. Let us know your goal and perhaps we can recommend one that suits your need.