As others have said, the problem with tiredness levels is that they have to be self reported: you can measure e.g. if somebody is anaemic or has some other condition which might be expected to affect their energy levels, but with two healthy people there are no measurements other than what they say they feel.
Now it seems perfectly clear that if you have two people faced with a household chore the person who will claim that s/he is most tired will be the one who wants the other person to do it. If s/he is willing to do the task, s/he will just get on and do it and you don't need the whole tiredness discussion.
We can probably also regard it as pretty common knowledge that the person who is most likely to experience household tasks as inordinately tiring is the person who thinks that s/he should not be the person to do them, that they are below his dignity, that they lie within the remit of the other person.
In other words, in households where at least one person has a sexist attitude towards household tasks, self reported tiredness levels are bound to fail. Doing something you don't want to makes you tired. Does that mean you should never have to?
People also have different pain thresholds and again this cannot be measured. And given that your pain threshold is something that one can to some extent work on (CBT has done wonders for my dd and the sheer responsibilities of fatherhood have done a lot for dh) it is debatable if you should try. Dh and I have the same cold: he makes more of a fuss, does that mean I have to do the housework?
My mother probably felt less tired with her bowel cancer than some other people would do with a head cold (because her expectations are lower and she doesn't like fussing). That doesn't actually mean that she should be picking up the slack for somebody with a head cold.
(btw not implying anything about my father here: he pulls his weight)