For me AH is about competition against live players and pretending to do a2a combat. In the beginning WB etc. were more roleplay/simulation, later on it became more a competition of skills.
On Minecraft I still haven't found a single thing that would actually look like fun. I'm trying to understand what it's about. Is there some kind of combat? 
Think of Minecraft like a sketchbook that requires certain skills to use. Alot of patience to acquire your pencils, some planning to map out your picture, and then alot of fun bringing it to life. Alot of people find great joy in creating wonderful things in Minecraft, like a 1:1 scale replica of the Enterprise D from Star Trek. Others like making castles, some like taking the simple in-game circuitry (Redstone) And building massive complex circuits, calculators, even TV's with programmed shows. Or using minecarts and railways to build huge rollercoasters.
Minecraft is a creativity box, a fairly good one. With monsters if you want them there.
There are two modes. Survival (Monsters, have to go out and farm your materials/mine materials to make things) Which is pretty fun, I'm in the process of building a large Wooden Longhouse on a hill surrounded by a wall.
Then there is creative mode where you can fly and spawn in any material you want in order to create things without having to go and mine out a continent of land to find enough gold to create a 90 Ft. golden...
object.
There are servers with PvP, servers with cities, one server is a replica of New York City.
It's an interesting game, and probably the most addicting 20 dollars I've ever spent.
