For this answer I am assuming that airships arent based on WWII technological limitations and are a developed, modern design, modern propulsion techniques and with modern materials.
Pros:
* its extremely resiliant to wind. Its limits will be the same as regular cranes. The load will start swaying too much above 30km/h and it becomes too hazardous to load/unload it as the windspeed increases, while a good airship will be able to handle air speeds up to its maximum speed. Unlike a regular crane, an airship could partially solve this problem since it could lower a straight and solid support down with the cables to minimize the swaying of the cables, meaning the airship would be able to work at higher windspeeds than regular cranes.
* an airship is the most stable of aircraft ever designed, even if we talk about WWII style airships. This is the one vehicle where the square cube law is a positive, as the wind can only push the surface area while the larger the airship gets the more mass is inside that needs to be displaced (it doesnt matter if its lighter than air, mass is mass!). 527
This means that it takes a LOT of wind and time to get the airship off position, and gives plenty of time for engines to correct the wind pressure. It also means that individual wind blasts are less influential.
* it doesnt take a lot of space. Cranes require space to set up and a lot of thought in where you set it up, the variable winds at different heights of the crane, counterweights, properly ankered into solid enough ground, the reach of the boom, minimum height the load needs to clear, possible necessity to anker the crane to nearby objects along its length. The airship can get there without impeding traffic and then hang above the target area where it is necessary. Since air traffic wouldnt be flying so low to a construction site it wouldnt impede airtraffic either.
* airships are perfect for construction in hostile environments or environments with low infrastructure where it is harder to get a crane to the location (although you could technically let the airship bring a crane and build it up at the location instead).
Cons:
* the airship needs to go off-station any time the stormwinds are predicted, where a crane can remain assembled (although a surprising amount of cranes fall over during storms, mostly due to human error building the cranes apparently).
* a crane just sways in the wind, an airship, even a tethered one, will need to use fuel or energy to balance itself and stay in position. The only way to avoid this is to build high poles and tether the airship tightly at its own height, or have many tethers in all directions so that the length of the cables limits the amount the airship can move off before several cables go taut. 308