Why doesn't the 744 fly this route for CX now?
Let's take United's KORD-VHHH which is the longest (non ER) B744 route in the world. (CX operates this flight with the -300ER)
Using todays Flightplan via POLAR 3 (G491) the planned distance is 7929NM. On average UA manages a ZFW of around 218,000kg. +/-5,000kg depending on the day(winds/route etc.). And this is using inflight redispatch.
UA's 744s have PW4056 engines, 396,890kg MTOW and 242,670kg MZFW and a average of 189T OEW.
Cathay has a mixed fleet of RB211 powered and (ex. SQ) PW4056 powered aircraft. The RR are a mix of 394T and 396T MTOW's and all the PW aircraft are 396T. IIRC MZFW is 242,670kg for all of them (same as UA's).
Considering that KJFK-KORD (using one of todays CX flightplans) is 8191NM the B744 simply wouldnt be able to carry the same payload that the -300ER does.
So not only does the 777 carry more payload on both routes, but it also does so burning significantly less fuel!
United's KORD-VHHH flight leaves with 20-30 seats blocked out (out of 374 seats) on the regular and almost always at max fuel. Same basic fuel capacity of CX's 744s. However keep in mind that every aircraft has slightly different tank sizes! A few years back UA spent a lot of time and money measuring these out across the fleet and N119UA was determined to have the biggest capacity out of the fleet, which today stands at 23 aircraft.
The B744 is a truly remarkable aircraft, however there are plenty of guys who can speak from first hand experience why the -300ER is better suited for these kind of stage lengths.