We have prepared comparable-diameter ZnO and Zn1-xCoxO nanowires with both circular and hexagonal cross-sections. The average diameters are similar to 113 and similar to 134 nm for cylindrical and hexagonal nanowires, respectively. The as-grown nanowires have been characterized via structure, electrical conductivity and photoluminescence (PL) spectrum measurements. Pure ZnO nanowires were Co-ion implanted to make magnetic Zn1-xCoxO nanowires for magnetization studies. Bumpier edge surfaces on a nanometre scale, higher densities of stacking faults and a bending feature along the growth direction have been found in cylindrical ZnO nanowires. As compared with hexagonal nanowires, we have observed relatively higher conductivities in cylindrical nanowires, which implied large numbers of shallow donors existing in the latter nanowires. The cylindrical ZnO nanowires also displayed intensified green defect emission and considerably more stacking faults in the crystalline structure. In addition, we have found increased magnetization and stronger ferromagnetic ordering in cylindrical than in hexagonal Zn1-xCoxO nanowires, and have experimentally identified that the point defects of either Zn interstitials or O vacancies played governing roles in ferromagnetism. We conclude that the cross-sectional shape effect originating a varied point defect density can profoundly modulate the structural, electrical, optical as well as magnetic properties of ZnO and Zn1-xCoxO nanowires.