Is it true that the higher the wattage for an electric bike the easier it will be for it to climb hills?

Is it true that the higher the wattage for an electric bike the easier it will be for it to climb hills? Or what other factors determine how well an electric bike is able to climb up hills?

I'm considering purchasing this electric bike which says it has a 1,000 Watt motor.

Does that mean that this bike will have an easier time of climbing hills than an electric bike with a 350 Watt motor?

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