"assuming equal power in both scenarios"
As Chris H said, pedaling power is usually understood as the power provided to the cranks, averaged over a full rotation, regardless of physiological efficiency. Same power = same speed if all else is equal (aero, incline...).
You probably meant "given the same level of exertion, how much faster will I go with clipless pedals?".
From what I read and based on my own mountain bike experience riding both types of pedals, going clipless gives you a power advantage during explosive bursts. This comes in handy on very steep technical climbs, when you need to pass large roots and rocks. Road riders will benefit from it when sprinting, or accelerating in trafic.
This study clearly demonstrates the power advantage over a 30s sprint:
The average across test riders is 617W with clipless, Vs 566 W using flats. That is a 9% advantage in power, which translates to a 3% advantage in speed.
Using the default parameters with this model, I get a speed of 50,7km/h with clipless Vs 49,1km/h with flats.
However, this extra power is not free, you will tire faster if you're using weak muscles to help stronger ones.
I could not find any study clearly demonstrating a speed advantage on a long flat course. Actually, "semi-scientific" videos like this one by GCN show that there is no power gain except in a sprint.
You might be wondering why everyone rides clipped-in at Tour De France or similar events. Riders spend most of the race in a peloton, shielding each other from the wind, with lesser team members taking turns at the front to help their leader. Whoever manages to save the most energy for the final sprint wins.