A rocket engine with a higher specific impulse doesn't mean it's 'more powerful'. That is, it will not make the rocket accelerate harder. In fact, the designs for engines with the highest specific impulse, like ion engines, are the 'weakest' of all types of engines. They accelerate the rocket slowly but steadily over a long period of time using only a tiny amount of fuel. In a race between two rockets with the same amount of fuel and two different engines the one with the more powerful engine will take an early lead, but when it burns down all its fuel, the rocket with higher specific impulse will still have some fuel left and will continue to accelerate. Eventually it will overtake its counterpart and will win the race if the distance is big enough for it to use its long-term advantage.
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