Both single and three core cables are installed in the Uk and the preferance varies between utilities.
The days of paper cables below 132kV are just about dead and the lower the voltage the colder the corpse.
Looking at cost first, three core paper cables were cheaper than three single core cables. Paper cables were provided with a lead sheath as a radial water barrier. Three core cables can also be steel wire armoured as the steel losses are small and do not have such a great effect on rating. Three core cables only need one cable entry into a termination box. Only one joint containing three cables at each joint bay (splice pit) means a smaller joint bay and lower cost. Pulling cables only requires one cable pull to install all three conductors. One duct (raceway) can contain all three conductors. Short circuit magnetic bursting forces are contained within the cable sheath. Shaped conductors may be used to reduce cable size. LPOF 3 core cables can utilise feed joints to reduce transient heating/cooling pressure effects.
Disadvantages of three core cables are that the individually the cables are larger and heavier than a single core cable which limits the length of the cable that can be installed on one drum before it exceeds vehicle height and weight. Manufacturers also have a limit on their drum twisting capabilities to lay up 3 core cables. The maximum conductor size of three core cables is thus lower than single core counterparts requiring more joint bays on a long route. Three core cable joints are more complex than single core joints.
Thus you would find that for small conductor installations 3 core cables were used and for large conductor installation single core cables were used.
Single core cables will be seriously derated by steel armour wire althogh aluminium armour is common. Larger conductor sizes can be handled, manufactured and carried with single core cables. Bigger conductors allow larger cable rating (ampacity). Single core cables can be installed in flat formation with spacing to allow better heat disipation and again a better rating. Induced voltages and currents in cable sheaths are important but there are ways around these on single core cables. Longitudinal water blocking of single core cables is easier to acheive.
Thus for low current short length requirements (e.g. industry) three core cables are "better" whereas for high power (e.g. transmission) circuits single core installations are more cost effective.
The relative cost of cables has reduced dramatically since the early days and civil installation costs have become more significant in Europe. Polymerics do not necessarily require a metallic sheath and where necessary low cost light weight radial water barriers are available.
This change in dynamic plus the development of polymeric cables has altered the cost balance but some arguements persist. The weight and size of cables per unit length still affect three core cable conductor sizes and typically 630sqmm is about the commercial limit.
There are other factors that may change the choice such as, a corporate stocking policy, spares requirements and special applications where, for instance, steel armour is required or where a triplex design is preferred.
Hope this helps.