Regardless of what you believe about androgen receptors, higher levels of testosterone - which males have - confer undoubted advantage, and studies have shown relatively "weak" men have had more strength than the strongest women in such surveys (which were of athletic samples). It is also the reason why testosterone is a banned ped and the IOC and IAAF have sought to restrict T-levels in female competition.
As I indicated above, a woman is only likely to be stronger by virtue of much greater size and muscle bulk - and relative youth - compared to the man. But many small men can, of course be incredibly strong- and not all older guys are weak either. T- levels are part of sexual dimorphism and most guys are stronger than most women. Perhaps female weightlifters as highly trained athletes, will be amongst the exceptions.