In small worlds, resources are closer together.
In large worlds, resources are farther apart.
According to the Terraria wiki page on World Size,
It also seems that in larger worlds, resources are much farther apart from each other in comparison to the smaller ones. This means that in smaller worlds, resources are much easier to locate and mine
This can be seen by using MoreTerra to display the whole map. Taking same-scale slices of each world size reveals the sparser dispersions of rare resources in the larger maps.
For a numerical argument, you could count the number of rare resources on n small worlds, n medium worlds and n large worlds. Then divide each count by the respective world dimenions and average the numbers. This method will give the average density of resources on each map size. The greater n is, the more accurately average resource density is estimated.
For example, below are three same-scale slices of each world size. Note, this is only one sample, so the total counts do not accurately represent the average resource density of each map size.
Small World
4300 x 1200 blocks
- Altar - 9
- Chest - 3
- Heart Stone - 4
- Shadow Orb - 5
- Amethyst - 16
- Diamond - 3
- Emerald - 9
- Ruby - 4
- Sapphire - 12
- Topaz - 16
- Total - 81
Medium World
6300 x 1800 blocks
- Altar - 6
- Chest - 3
- Heart Stone - 2
- Shadow Orb - 7
- Amethyst - 5
- Diamond - 0
- Emerald - 1
- Ruby - 1
- Sapphire - 2
- Topaz - 5
- Total - 32
Large World
8400 x 2400 blocks
- Altar - 2
- Chest - 0
- Heart Stone - 3
- Shadow Orb - 9
- Amethyst - 2
- Diamond - 1
- Emerald - 1
- Ruby - 1
- Sapphire - 4
- Topaz - 2
- Total - 25
Symbol legend
Another way to find the exact dispersion ratio is to look at the code.
In response to people asking about an open source version of Terraria, Redigit says,
This will probably happen eventually, but the decision to not obfuscate Terraria was made for a reason
So until the open source code is released, somebody could dig through the decompiled code and find the variables that control the base resource density of each map size.
Best Answer
For weapons and armor, they all become useless eventually. Once you've got full adamantite armor/weapons there's no higher tier to mine and there's no point to making more of what you already have. However, even the lowly copper remains useful for watches, depth meters, timers, and hardmode boss summoning items. I'd suggest keeping one hundred bars of each metal from copper to gold on hand and sell the rest. If you want to know what you can make from each kind of bar you can use the guide or the wiki.