I will not let this go without a final comment.But an objective measurement of the performance of the old, scaled up, element deficient shower would show that it was not performing as well as the new smaller one.
All they knew was they successfully had a shower, just as they has for a period of time without noticing the gradual reduction in performance. The next time they needed a shower it didn't work.
The new pristine unit outperformed the old petrified unit. As far as the user was concerned their perception was exactly that and quite rightly so in the circumstances.
The technical statistics has absolutely no bearing or influence on their ablutions each side of the repair, all they were interested in was the improvement.
I'm quite sure exactly the same reaction occurred the next time it was changed, presumably for a >10KW where the ignorant fitter will have extolled the virtues of the higher costs. Apologies if the latter comment does not apply.
Incidentally a trawl trough a selection of manufacturers specs certainly does indicate that all electric heaters are not equal.
In a different genre there is a lot of calculation involved with heater batteries in AHU's, whereby the thermal efficiency of different power elements and their physical size will dictate the selection used and I have worked on systems where 2 batteries of different powers are doing the same job but in different size ducts. But this is a whole different ball game.