In US Cities, the answer is...
... it depends. Most US cities don't have the layout restrictions that many European cities do, i.e., our streets are laid out in a grid, are wide enough to accomodate truck traffic in both lanes (although most will have problems if the truck is parked). There's also the weather extremes that are common in the US which, until recently, were unknown in Europe. A truck (or lorry) can still make a delivery when the snow is falling at 3 inches (6 cm) per hour; a bicycle (or tricycle) is less certain under those conditions.
Still, there are industries and situations that can use a cyclist for delivery. I used to work for a hydraulics/pneumatics company that had several local customers. If we had to deliver parts to one of them, we would call a local taxi company to do the delivery. In a situation like that, the cyclist might make the better choice (if it's not raining, snowing, etc.)
