I have some notes on all the Genesis metals... I think most of this is from around 5.30 so there's a chance something's changed since I last read through the raws.
Copper, Iron, Steel and Adamantine are the same as in Vanilla, so I compare everything else to these metals.
Cobalt: About as good as copper for weapons and armor generally, meaning I never use it unless it's all I have. Can be very plentiful though, it's great for making BLUE furniture and bolts. Same weight as copper.
Titanite: If you have magma and find veins of the right rocks, titanite is incredibly good and easy to make. Equivalent to steel for armour, at half the weight. Twice as sharp as steel, or half as sharp as adamantine, however you want to look at it. Titanite ores: Anatase, Ilmenite, Meteorite, Rutile, Sphene
Bloodsteel: twice as sharp as steel (a bit sharper than titanite), same weight as steel, between steel and mithril on armour attributes. Is actually a boring grey colour, despite what the name may suggest.
Voidsteel: only slightly sharper than steel, otherwise the same as bloodsteel. I've been told it does extra damage to voidlings but haven't tested those guys in a while and they've been changed. Other notable difference is bloodsteel uses bauxite where voidsteel uses obsidian. This makes voidsteel much easier to make.
Mithril: It's like a poor man's adamantine. Same weight, half as sharp (equal to titanite) 2/5 as good as adamantine for armour (twice as good as steel). Can be made into clothes like adamantine. Rarity depends on how much silver and aluminium you have on your map, although you can import both of these if you need to.
Vulcanite: Similar stats to adamantine, although it's nearly as heavy as silver, and 30% sharper. And it's RED!
Dragonscale/Dragonbone: Dragonscale is for armour, dragonbone is for weapons. Slightly heavier than adamantine and lighter than titanite. Armour stats slightly worse than bloodsteel vs blunt and equal to steel vs sharp. Dragonbone sharpness is between voidsteel and titanite. The only way I ever have any is from melting stuff traders bring me. Also, there is a leather called dragonscale... this one is a metal bar.
Moonsilver: A weird one. Supposedly the metal to use against werebeasts and the like. The numbers in the raws suggest that it would be either worse than copper or between copper and steel as armour, and it has no value for MAX_EDGE which is what I use to judge sharpness/axe quality. I've never really used moonsilver so don't know much about how well it actually works.