To first understand the rest of the blog we must first understand the rarity of iron and diamonds. First, there are about 77 blocks of iron ore from Y coordinates 1- 63. There are about 3.097 diamond ore per chunk from Y coordinates 1- 16. Now let's say you made a branch mine that was made of 1x2 hallways on layers 11 and 12 (the best hotspot for diamond).  When you do that you reveal about 1 and two thirds layers of a chunk including the floor and ceiling. To get the best guess of how much iron you will find we first must find out what percent of iron spawn layers we are uncovering. About 5.73% of iron spawn layers are uncovered. It would then be logical to assume that approximately 5.73% of iron in the chunk would be found. 5.73% of 77 is rounded to 4. While four is the amount you will likely uncover, it is not the amount you will get. There will likely be a whole vein of iron attatched to the iron ore you uncover. There is an average of 7 iron ore in one vein. That would mean you would likely get plus or minus 28 iron ore per chunk you mine. If we go through the same process for diamond ore, we get about 4 diamonds from a chunk (There is an average of 5 ore per vein). 

Ore	Ore per Chunk	Ore per Branch Mine in Chunk
Diamond Ore	3.079	28
Iron Ore	77	4

Now let's look at tools. All Iron tools have the same statistics as do diamond tools. Iron tools have a base mining speed of 6 and diamond has 8. That's a 33% increase from iron to diamond. Iron tools have a durability of 251 uses and diamond tools have a durability of 1562 uses. That's a 722% increase from iron to diamond! Now that we know this, would it be better to use diamond or iron tools? Iron tools can break stone in 0.375 seconds. Diamond can break stone in 0.281 seconds. To see how breaking speeds work in Minecraft click here. When you make an effictient branch mine, you essentially mine out a third of the blocks on two layers. Basically you would mine out 170 blocks.  That would mean that an iron pickaxe could mine out 1.48 chunks in a branch mine for about 41 ore in 1 minute and 34 seconds and a diamond pickaxe could mine out  about 9.19 chunks for about 36 diamonds in seven minutes and 19 seconds. 

Tool Type	# of Chunks Able to Branch Mine	Time to Branch Mine Those Chunks	Amount of Ore Obtained
Diamond	9.19	7 minutes 19 seconds	36
Iron	1.48	1 minute 34 seconds	41

Now what about armor? Here are the stats for armor:

Armor Piece	Durability	% of Damage Absorbed
Iron Helmet	166	8%
Iron Chestplate	241	24%
Iron Leggings	226	20%
Iron Boots	196	8%
Diamond Helmet	364	12%
Diamond Chestplate	529	32%
Diamond Leggings	496	24%
Diamond Boots	430	12%

At a first look, it would seem that diamond armor is definitely better. But is it really? Let's say you are being hit by a mob once a second that takes away 50 hearts (100 health points). Let's also say that this mob is hitting every piece of your armor each hit. Here's how long your armor would last:

Armor Piece	Time Until Broken
Iron Helmet	20 seconds
Iron Chestplate	10 seconds
Iron Leggings	11 seconds
Iron Boots	24 seconds
Diamond Helmet	30 seconds
Diamond Chestplate	16 seconds
Diamond Leggings	20 seconds
Diamond Boots	35 seconds

As you can see, diamond lasts around 1.5 times as long as iron does