Having done several studies comparing the two types, it is apples and oranges, cannot bluntly state that one is more economical than the other, it all depends on the role.
The ATR is unbeatable in seat cost for stage lenghts under 500 NM in high infrastructure cost (airport & navigation fees) environments like Europe. The ATR 72 has the lightest airframe weight per seat of any airliner in operation, period (beating the 380 & 787 too). However its cost advantage starts disappearing quickly on longer routes due to the low speed, as hourly costs (crew, mainenance, ownership) start kicking in.
The Q400 was designed to compete with jets on under 1000 NM stage lenghts, where the speed disadvantage is not so significant commercially, however fuel economies are major (at time of launch trip fuel was about 50% of that needed by similar capacity jets, eg Fokker 70). Modern RJ-s have eroded this cost advantage, and the ERJ comes very close to the ATR-s empty weight per seat figure, leaving less role for the Q400.
On the other hand, there is nothig remotely similar on the drawing board to challenge the ATR on short regional routes. However the main competition on such short sectors is now high-speed train, not surprisingly most ATR sales these days are to regions with no such rail infrastructure.