To put in the perspective how much powerful is the firehose versus tap water stream? ?

In the city the firehose comes from the same mains as feeds the house.  So the pressure at the nozzle is the same as that of the tap confined through a nozzle.  The difference in force is due to the AREA of the nozzle.  However in modern fire engines they draw water from the mains then pump it to increase the pressure.  If you don't confine it in a nozzle much of the pressure is lost in the friction in the pipe so the pressure and velocity of the water leaving the tap is a lot lower than that of water leaving a nozzle.

If you take philomel's numbers the force of the water would be proportional to the pressure * Area ( a standard physics formula after all)  So estimate the ratio of the areas of the two nozzles and multiply that by the ratio of the pressure.

A fire hose pump can  pressurize the hoses to 600 to 900 PSI.

Tap water pressure is around 40 to 60 PSI.

The difference is not calculable without more info.