There is no fixed relation between pressure and flow. If you combine both and let the same stuff flow through both pipes, you can see a pressure difference.
Think of it like this, with a flow thick pipe -> thin pipe: The material has to increase its velocity at the boundary (as you have the same flow in both pipes). This requires an overpressure in the thick pipe. In the reversed flow direction, the material does slow down, this corresponds to a higher pressure in the thick pipe, too.What you probably mean is the pressure drop per length in the pipes: This is lower in the thicker pipe, as the resistance to flow is lower there.