Heard it best described this way on a TV auto show over the weekend. A turbo takes in air and puts out happiness!!
At all operating RPM a turbo is more efficient than normal aspirated engines. However, as posted above like any other engine gentle acceleration will yield slightly better fuel economy. Apples to apples the first gen ECO boost 4 cylinders had a bit more horse power than the prior years V8 and got better economy across the board
We can get esoteric and discuss time spent in lower gear versus time spent higher gear. Some folks believe that acceleration at a slightly harder rate will get you into a higher and more economical gear ration quicker therefore negating the excess consumption.