You realise you've opened up a big can of worms here?
You will find that everybody has an opinion on the "best" bike - and they are all different.
What do YOU want out of a bike - are you solo or two-up? Are you going to stick to the main routes only, or are you going to go into the far back-country and do some serious exploring? What is your riding ability and experience?
As a GENERAL guide, here are my observations that seem to be pretty much in agreement with most peope.
If you want to stick to the good main roads, and are two-up - or solo - the Tiger will do fine.
It's negatives - very heavy, and not much of an off-road bike. The Triumph is very top-heavy and doesn't work well off road.
Positive - excellent reputation for reliability.
Negative - not likely to find much in South America in the way of parts or service. However, the internet and airplanes can get you just about anything in a couple of weeks.
Luggage - to my knowledge, and I have NOT researched it, the only stuff available is the factory plastic stuff - not adequate. However, there are plenty of people making alloy bags that can make a good rack for you for their bags. Check my links page for info.
If you want to go the nasty road / backcountry explorer route, the KLR is the best choice, and is a good solid reliable and proven bike.
The R80/100GS's are good allrounders, if you're two-up and want to off-road it a bit, it works well and is cheap. There is a ton of aftermarket gear for them, you can get just about anything you can imagine. Parts availability is very good, even in South America, although much cheaper if you bring it in yourself.
The R11xxGS's are better on-road, much faster, newer, work shockingly well off-road for their size and weight, but are expensive and have to be set up right, depending on which exact one you have. There is also a lot of aftermarket gear for them. Fuel mileage is BETTER - s;ightly - on them than the R80GS.
In the end, you can do it on anything, people have gone around the world on everything from a Honda 50 Cub to a Harley, and one of those was a guy with no legs. A guy recently did Alaska to Ushuaia on a Velocette, and another guy is going around the world on a BSA B31. Two-up.
Decide what your priorities are, and choose accordingly.
Have fun, and let us know what you decide!
Remember, these are opinions - don't anybody go getting all offended now! What's YOUR opinion?
Share the Dream!