The 767 has/had a few shortcomings compared to other twin aisles. First and foremost, it was designed in 1982 and it was primarily designed for trans-continental flights, competing with the A300 and DC-10 and replacing the L-1011. It had a smaller diameter 7-across seating fuselage vs. 8- or more across of the other twin aisles. The smaller diameter meant it could not carry the standard LD-3 containers for baggage and cargo that all other twin aisles used.
This was a factor for Northwest Airlines, a major international cargo carrier, when it came time to replace it’s DC-10 fleet. For international service they chose the A330 which used the same LD-3 containers as the DC-10 and their 747’s. For domestic service, where cargo is less important, they replaced the DC-10’s with 757–300’s.
The second factor was range and extended twin engine operations. When the 767 was developed twin engine airplanes were restricted to flying no more than 60 minutes from an airport in case of emergency. With ETOPS (Extended-range Twin-engine Operations Performance Standards), this was increased first to 120 min, then 180 min and ultimately to 207 min for the 777. This allowed twin engine planes to fly trans-Atlantic, but the 767–200 lacked the range. Boeing’s solution was to introduce the 767–200ER (Extended Range). But the A330–300, which began operation in 1994, was a superior aircraft for intercontinental routes. The third limitation was that it did not have a fly-by-wire control system that the A330’s had.
Boeing’s answer to these problems was to create the 777, which entered service in 1995. It is a larger plane made possible by the development of much more powerful engines. It was designed from the beginning to take full advantage of ETOPS. This addressed all three deficiencies of the 767: it used LD-3 containers and was Boeing’s first fly-by-wire design. The introduction of the 777–300ER, it now had the range to open up trans-pacific routes to twin engines, and ultimately became the replacement for 747’s.
However, the A330 continued to sell well, filling the role as a medium sized twin aisles with good range. The 767 ultimately became a model that was primarily used by US carriers. Boeing’s answer to this was to develop the 787 which is a medium sized twin engine with excellent range, and of course was fly-by-wire and used LD-3 containers.