The key benefit of Luffing Jibs, is their ability to park at night in a smaller radius. When a crane is 'out of service', it's a requirement that it is able to 'weathervane'. This means that in high winds, the jib must always rotate such that the jib is facing downwind, and the ballast serves to counteract the rotation force of the wind. Consequently, it must be impossible for the jibs to hit one another, whatever direction they are facing. For multiple 'saddle jibs' (classic T shape), they get around this by setting the jibs at different heights, so that they overlap. They still can't have the towers close together than the length of the lower jib, however.
With the increase in pre-fab, it's often desirable to fit more towers onto a single site. Furthermore, strict overhanging regulations in cities may prevent you from siting a saddle jib close to the boundary of your site, in case it swings over (or hits) neighbouring buildings when free-slewing at night. A luffing jib can be parked at a steep angle, and thus with this smaller out-of-service radius, you can fit more cranes onto the site, and stay within the overhanging regulations.
There is a trade-off, however. If you try to park your jib at too steep an angle (over ~60degrees), the jib no longer has enough leverage to rotate the slew ring around under wind load. This is why you now sometimes see a solid 'rectangle' in the tip of a luffing jib. This is a 'windsail', and is literally a sheet of steel (sometimes fabric) designed to increase the surface area that the wind can push against, allowing an even smaller park radius compared to a traditional luffing jib.
If you want to go tighter still (over ~75degrees), you need more area again, but, if you have a large fixed sail, that would make driving the crane in service very difficult under a light wind, and would limit the maximum wind speed under which it would be safe to operate the crane. The solution is to have a retractable windsail, which is deployed at night, and retracted when the crane is in use.
his innovation was a key part in Select Plant Hire being offered the contract to supply cranes for the Shell Centre on London's south bank, which had 21 cranes on a single site, 17 of which required retractable windsails. This allowed them to offer a faster production schedule than other companies that couldn't get so many cranes into the space.
As far as I'm aware, saddle jibs are just more simple, and consequently a bit cheaper to use, and are used where possible by default. When you see a mixture of cranes on site, it's likely that the luffing jibs are sited near the edges, where overhanging regulations are an issue, with saddles in the middle to save money.
