>>1288193-200 and -300 models of the A340 used the CFM56 engines, the same as were used on the 737 and A320. 2 CFM56s have an approximate fuel consumption rate of 2 tonnes an hour (compared with the 4 GEnx engines consuming 12 tonnes of fuel an hour on the 747-8).
The -500 and -600 models featured Trent 500s which had a higher thrust rating, but a slightly higher fuel consumption (for a larger, longer aircraft, which meant that fuel consuption per seat was about the same). I'm not sure what the fuel consumption rates of the Trent 500 are compared to something else.
Interestingly, an A340-200 would probably have a comparable fuel consuption rate to that of a 787. However, the added maintainance of 2 extra engines complete with the fact that the older A340 has lost a certain amount of its efficiency means that the 787 has an edge in most aspects..... except capital costs. A second hand A340 would be a lot more cheaper than a 787 brand new. This is also why IAG budget airline, LEVEL, has been able to be so cheap with just A330s for transatlantic flights, they're using cheap, second hand A330s which offset the fuel savings a 787 might offer based on low capital costs.