I am no engineer and my grasp of physics is pretty limited, so I can only imagine that it is to do with levers. If memory serves, the further a lever point is away from its load the stronger it becomes. There is of course a happy medium because you have to take into account the strength of the metal in the crane, and the weight of extra metal and so on.
The curved crane is probably a way of getting the height of the lever point further away from the load wihtout having to get the engine and driver so far up in the air.
What really used to get me was how they built themselves. They're built at ground level ish by a couple of mobile cranes, and then they build themselves, jacking up the whole structure within their own internal hydraulics and inserting another piece of body.