Why do men have a higher hematocrit (red blood cell count) than women?
I found a nice article that has insights to this matter. As posted before me it is true that only adults, but not juvenile individuals show this difference. Direct and indirect effects of sex hormones on bone marrow erythropoiesis and renal erythropoietin production has been proven, but it works in both sexes the same way. Females are capable to elevate their haemoglobin / red blood cell levels to external stimuli, yet at same conditions (same altitude etc) the difference remains. Also:


  Men, premenopausal women and postmenopausal women have similar plasma erythropoietin levels, indicating that women do not attempt to compensate for their lower haemoglobin levels by increasing erythropoietic drive. These observations show that the prevailing lower haemoglobin level in females cannot be ascribed to a lack of bone marrow or renal erythropoietic capability: they indicate that adult females maintain their venous haemoglobin levels at a lower level than adult males as a physiological steady state — they do not try under physiological conditions to maintain the same levels as adult males. 


This could be achieved by modulation of the juxtaglomerular apparatus signal (JGA) of the kidney. The JGA has important role in the regulation of the haemoglobin level - it is the main input for erythropoietic red blood cell production by regulating renal filtration and thus regulating the amount of oxygen that gets to the EPO producing peritubular cells.

It is noteworthy to say that similar difference exist in mammals and even there are examples among birds and reptiles.

It is described in the linked paper that both men and women achieve the same or very similar microcirculatory haematocrit level inspite the different mean venous haemoglobin levels. 

This implies the very interesting theory / reasoning in the article:


  (...) that both sexes set their mean optimum level separately and to some degree independently.(...) the red cell mass is an enormous resource in animals — one third of the body's cells by number in adult humans, and demands enormous effort to establish and maintain.(...)This price must be paid for by increased fitness.(...)The excess red cells over the critical minimum that circulate in the large vessels (and slowly through in the spleen in some species) and that constitute half or more of the venous haemoglobin level probably provide a storage function for the reserve red cell mass for use when the need arises for increased work — fight, flight, food and reproduction. They may also act as reserves for heat exchange and iron storage. It is likely that the return in fitness from this reserve differs between the sexes, and therefore that the optimal size for maximal cost benefit also differs.