When he made a video on the topic, Jason Slaughter of Not Just Bikes preferred two wheels with the big box upfront (bakfiets):
* https://www.youtube.com/watch?v=rQhzEnWCgHA&t=2m55s
* https://en.wikipedia.org/wiki/Cargo_bike#Long_john_bicycle
The three-wheeled ones take some getting used to. You can't take turns at a high speed or you'll tip over. They are nice when you are standing still, because they stay up-right. They are easier to turn-around on foot: the front wheels are closer to the centre of mass, so you can easily lift the back wheel and swing it around.
The two-wheeled ones are faster, and handle more like a normal bike. When fully loaded (100+ kg) they take some effort getting them on the stand. They are clunkier to turn around.
I prefer the two-wheeled ones.
The nice thing about the three wheeled ones is you don't need to use a kickstand, though the two-wheelers tend to have really solid kickstands.
That thing was a slightly faster and more ergonomic wheelbarrow, not a bike.