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.
The risk with the three-wheeled ones is that they are perfectly stable right until they aren't. You're either upright or on your ass. The steeper you turn the smaller the stable area gets, even when going slow. The two wheeled ones have more of a gradient. You'll feel it when it starts to go so you can course-correct.
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.
I've only done the three wheeled one, and that is a never again. It's like training wheels. You can't lean in a turn. Besides that, the steering was weird because there wasn't an axle, instead the entire middle of the frame was articulated.
That thing was a slightly faster and more ergonomic wheelbarrow, not a bike.
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