KLM is currently the only airline with a full Business Class service on SCL-BUE, Delft House included.
LA (and AR) treat it as a "regional route" so they only offer Premium Economy, even when using widebodies. LA is starting a new SCL-EZE-MIA rotation in December - I don't know if they count on offering Business Class on the SCL-EZE sector as well.
I find it too short of a flight to enjoy a lie-flat seat (and I'd always prefer AEP to EZE when going to Buenos Aires), but if Business is what matters, then go with KL.