Thaumcraft is a the more intense of the two mods in this list. It adds a few ores, some machines/devices, magic, research, adventure purpose, a cult, ancient mysteries, etc to the game. It is also fairly complicated, requires you to advance through research to uncover abilities and recipes, and can be quite resource intensive.
In thaumcraft you break down objects into their base essences, store the essences, and use them as crafting components. You can create golems to do your bidding or enchant blocks and paths to make them invincible or block monsters from crossing your threshhold.
Thaumcraft introduces viz which is primarily produced via aura nodes that are found throughout the world. This is the power that charges wands and staffs. There are a number of different types of viz and most nodes do not have all types so you have to venture out to find nodes that will allow you to recharge your magic quickly. Later in the game you can move the nodes around so you can make central charging facilities.
Witchery encompases ritual magic, voodoo, and herbalism. You brew potions, perform ritual spells, and make an altar to fuel your magic. Witchery allows players to mess with each other, or help each other, using voodoo. This can be humorous or irksome but it isn’t boring.
In witchery you grow herbs in gardens to use as ingredients for your spells and items. You draw ritual circles and create talismans and such to use with them.
Witchery power is generated by an altar that you can craft very early on in the mod. The altar draws its power from the world around it, primarily the plants within some radius of the altar. That radius can be changed by placing certain objects of power on the altar, or the altars power multiplied in a similar way.