To sum it up: AA First gives you more space and a better presentation of the food; LAN Business is more comfortable because soft bedding and large pillows are supplied for sleeping, LAN wine is better. If all else is equal I would take an extra pillow and fly AA first; if AA First is more expensive or less convenient than LAN Business due connections or timing, I would prefer LAN Business. AA Business is completely different due to the angled seating. LAN Business is preferable to AA Business under almost any imaginable scenario.