Range of the aircraft, you won't get a 757 from LHR - SIN (although some US carriers do push its range to the limit).
Availability of a fleet - whats in the hangars, whats needed on other routes. Cathay are renown for "misusing" their fleet. A 747 on the ground between long haul rotations may be put on a short round trip to Taipei.
Need for frequency and even babysitting slots (look at UA LHR - EWR, 1 x 777, 4 x 757 daily). This is an extreme example but operating many long haul routes daily is a commercial necessity.
Lack of slots at certain airports and in a few case bilateral constraints on frequency.
Mix of classes - some types may have a higher or lower proportion of premium seats. BA 767 / 787s do not have first. LH I believe have a higher proportion of premium seats in their 747s than A380s.
Desire to put newer aircraft on flagship routes.
Cargo capacity - don't overlook belly cargo on certain routes.
Operating & capital cost. Expect to see BA 77Ws achieving high utilisation - the fleet its got high capital costs better but fuel efficiency and lower maintenance costs than their 744s and can cope with long ranges.
In the case of US carriers the location of crew bases could play a part.
I'll probably think of a few more.