help physics please?

We cannot argue this in general. We can only make specific assumptions and carry that to a conclusion.

For example, Steve assumed climbing stairs. In which case QE = Mgh and qe = mgh are the big M and small mass m < M work cases. Clearly QE > qe and the obese one does the most work.

But we cannot say that about the power as that's energy expended over a period. So here, for M and m, we could very easily have P = mgh/t and p = Mgh/T where the slim Jim expends less energy but in a much shorter time t < T. And at some point that's more power for the little guy.

And of course, both M and m, could very well be walking on the straight and narrow, with incline. In which case, the work would be qe = fS and QE = FS where f = kmg and F = kMg is the friction force for m and M as both trod over S distance.

We see here that qe < QE because slim Jim does not need to push off against as much friction force as the tubby one, M, to walk forward. But what if the two guinea pigs in the experiment are walking on different surfaces; so the coefficients of friction, the k's, are different values? That could very well alter the outcomes of energy and power.

Anyway...bottom line...we cannot argue one way or the other without more specifics.

The statement is true only if the experiment involves running up a flight of stairs in a specified amount of time.

We can't know what is correct for "this experiment" if you don't tell us what "this experiment" is.