How is the Dash 8 Q400 so fast?
Here are the cruise performance tables for the Q400 at the heaviest and lightest weight (click to view larger):
Source: from the Dash-8 Q400 performance manual, which came included with a simulator product I purchased. They probably got their data from a QRH (Quick Reference Handbook), which usually includes such tables in the In-Flight Performance section.
At ISA conditions at FL250, the long range cruise is flown between 209 and 188 KIAS (depending on weight) and the high speed cruise is flown between 230 and 243 KIAS. The corresponding TAS at FL250 (assuming ISA conditions) are:

188 KIAS: 281 KTAS
209 KIAS: 312 KTAS
230 KIAS: 343 KTAS
243 KIAS: 363 KTAS

That last value (for high speed cruise at light weight) seems to agree quite well with the max. cruise speed of 360 KTAS, which one usually find for the Q400. But best range speed at that weight would be around 188 KIAS (281 KTAS), quite a bit slower. At higher weight, the speed differences between best range and high speed cruise are smaller though.
At typical weights the Dash-8 will still be faster than the ATR 72-600. I don't have exact performance tables for that aircraft, but Wikipedia says cruise speed is 280 KTAS. So yes, the Dash-8 is built for higher speed. The biggest difference is the choice of engine: PW150A with 3782 kW for the Dash, but PW127M with only 1846 kW for the ATR, more than a factor two difference! While this difference probably causes a higher best range speed for the Dash compared to the ATR, in absolute fuel usage the ATR is still more economical.