Well I can explain you the difference.
Tier 1 chests contain: raw food, sticks, feathers, flint, fishing rods, wooden (stone, not sure) swords/axes, leather armor and iron ingots.
Tier 2 chests contain: Cooked food, golden apples, diamonds, iron and gold ingots, boats, clocks, compasses, iron/chain/gold armor, stone swords.
Tier 2 chests are mainly found at the cornucopia and hard to reach chests. (think of puzzles or at the top of a large building)