In late 80s, Cathay was in dire need of an L-1011 replacement. The A330-300 was available and met Cathay's needs. At that time the B777 concept wasn't even well defined, so the A330-300 got the nod. When the B777 program came a few years later, Cathay's team really liked the aircraft. They were particularly interested in the proposed stretched version that they envisioned as a B747-200 replacement. However, Boeing didn't have a definitive timetable for the stretched version. Cathay got on board with the B777-200 so they could have their voice heard and pushed for the -300 launch. For example, the fuselage width was widened at Cathay's request of having the option to configure ten-abreast seating in the economy section. Nevertheless, the B777-200 is too close to the A330-300 in terms of capacity and range. This is the reason why Cathay has a small fleet of five -200s. Cathay launched the B777-300 in 1995(?) and converted seven of their original 11 -200 orders to the -300.
Before the early 90s, Cathay's long-haul strategy centered around the B747-400. Although the Cathay Team liked the B777, they would not consider the B777-200ER because of their conservative views on ETOPS issues. IIRC, in 1993, the financially troubled Philippine Airlines unilaterally cancelled their orders of 4 A340-200s without much notice. Airbus was eager to unload those 4 -200s. Somehow, they got Cathay interested in the -300 and gave them a very sweet deal. In return, Airbus asked Cathay to take the 4 PAL -200s in the interim before Cathay got their own -300s. (Eventually, Airbus was able to get PAL to take the -200s after Cathay got their -300s.) Since then, Cathay realized the flexibility of the smaller A340, and their B747-400 fleet size has stayed flat for many years.
A few years earlier, United started flying non-stop between Chicago and Hong Kong with the B747. The service seemed to be a hit and Continental decided to offer Newark-HKG nonstop with the B777 and United quickly countered with JFK-HKG nonstop with the B747. Although Cathay had flown a few experimental HKG-JFK nonstop flights using the polar routes, Cathay felt the payload restriction of the A340-300 and B747 on this route would make the service not viable. So they arranged with ILFC to lease 3 A340-600 for this route. However, apparently CO and UA were taking too much premium traffic from Cathay, Cathay decided to lease 3 ex-Singapore A340s from Boeing and configured the aircraft with around 180 seats. The aircraft was delivered right around Aug/Sept 2001. UA withdrew their JFK-HKG service before 9/11. After 9/11, CO withdrew, too. So, CX never started the JFK-HKG nonstop service. Now, there is no pressure to start the nonstop service, so the newly deliver A340-600s have been deployed on other routes.
Here's the history of CX's fleet selections. I'll let you decide what the advantages and disadvantages are.
