I expect vesicle formation and fusion to require energy input; however, I'm not sure about which of endocytosis and exocytosis require energy and how they use the energy input.
Do they belong to active or passive transport?
Exocytosis... is the durable, energy-consuming process by which a cell directs the contents of secretory vesicles out of the cell membrane and into the extracellular space.
Endocytosis is an energy-using process by which cells absorb molecules (such as proteins) by engulfing them.
Emphasis mine. Here's a nifty paper which gave some evidence a few decades ago for some basic intracellular thresholds for budding and fusion, and this paper shows that endocytosis definitely requires ATP, using a novel assay. Check the sources, too, some of them are excellent.
Just to extend the answer from @Amory slightly, I think that the terms active and passive transport are best kept for describing transmembrane movement of molecules.
In the case of exocytosis the only transmembrane event is when a secreted protein is first inserted (usually cotranslationally) across the endoplasmic reticulum membrane. I'm not aware of any evidence that this uses more energy than that already expended during polpeptide elongation by the ribosome. At that point the secreted protein is topologically extracytoplasmic, and everything else is achieved by rounds of vesicle formation and fusion of vesicles with target membranes.
The same is true in reverse for endocytosis. Any molecule that is internalised in an endocytic vesicle is still extracytoplasmic unless some process specifically moves it across the membrane of the vesicle, or a downstream organelle such as the endosome. At that point whether the transport process was active or passive would depend upon the properties of the carrier system.