....I do have the time but not very handy...
The 2stone would be a very good investment. It is a proven, rock solid pizza cooking machine. Propane is hot and fast, and it is very user friendly.
The Big Green Egg is also a rock solid cooker. Some people have adapted its excellent cooking characteristics to cook pizza. It burns lump charcoal as Chau said above. It requires maintenance, that the 2stone would not, just to cook a pizza.
You are really asking about apples and oranges. If you want a dead set pizza machine, go with the 2stone. If you are willing to accept a learning curve, and experiment, and be able to bbq, the go with the green egg.
For whatever its worth, I felt that the 2stone was probably the best 'nut cuttin', no holds barred, Katy bar the door, drop dead legs, pizza oven ever; and decided I wanted one very badly.
Just my two cents.