Suppose we have $100$ people and we obtain the average blood pressure $x$. Now suppose we have another group of $40$ people and they have an average blood pressure $\approx x$. How do we quantify the fact that the second experiment is more "efficient" than the first experiment? Would we do a power analysis? What would be the null hypothesis?
You didn't get the same information: you got a confidence interval of a certain width from measuring 40 people, and then after measuring 100 people you got a confidence interval of a (probably) much smaller width- that's information.