Whilst they do have a much smaller span, they normally have a much greater draw weight to compensate. This is why crossbows often required a complex winching system to reload them - they were that overwrought, they needed a lot of mechanical power (and time) to draw them back.
A longbows max drawstrength was 200N, compared to the most powerful crossbow's (the Arbalest) max, of 22kN. That is somewhat more than "3 times the draw strength". Thisridiculously high draw strength more than compensates for teh crossbow's shorter span and lighter darts. Even if you assume the OP is referring to standard, early crossbows, the power of a typical crossbow is marginally greater. The range of early crossbows is less than that of longbows, but crossbows developed considerably, increasing in range and power. It was specifically the crossbow's penetration power at closer ranges (and not the bows's) which led to heavier and heavier armour.