Learning Elixir - gives a 20% boost to xp. Basically multiplies all xp you earn by 1.2 for the duration (which is 2-3 minutes, not 30 seconds....still quite short, but a handy boost for turning in several quests at once in co-op, or for a horde night or something). a 500 xp zombie will give 600 xp. mining and getting 10 xp will give 12.
Fergettin elixir - refunds all your skill points - including points earned through the tutorial quest. You keep all recipes learned through schematics or books, you keep all book unlocks. Anything currently crafting will finish crafting at it's current quality. You will lose the ability to craft skill-granted recipes that you don't ALSO know through a schematic (such as if you know the forge through advanced engineering 1, but haven't found the individual forge schematic). You can then spend those skill points on whatever you want immediately, and permanently (until you drink another fergettin' elixir)