The oxides of the SrCo1-xSbxO3-delta perovskite family have been recently designed, characterized and described as cathode materials for solid-oxide fuel cells with competitive power performance in the temperature range 750-850 degrees C. They feature a number of interesting properties including a good electronic conductivity, low electrode polarization resistance and adequate thermal expansion; the crystal structure adopts a 3C corner-linked perovskite network with a considerable number of oxygen vacancies. This paper reports on the effects of Sb-doping on the crystal structure features, the Co oxidation state and magnetic properties related to the presence of spin-state transitions in the Co cations. A phase transition was observed from the tetragonal P4/mmm space group for x <= 0.15 to the cubic Pm (3) over barm space group in the x = 0.2 composition from neutron powder diffraction data. For the tetragonal phases the oxygen vacancies were found to be ordered and localized in the axial O2 and equatorial O3 atoms surrounding the Co2 positions. A noticeable distortion of CoO6 octahedra is observed for x = 0.05 and 0.1, exhibiting a charge-ordering with a mixed oxidation state of Co3+/(4+) at Co1 sites and Co3+ at Co2 positions: the Jahn-Teller Co3+ in an intermediate-spin configuration is responsible for the octahedral distortion. Increasing Sb contents promotes a higher average oxidation state of cobalt, from a valence of 3.2+ for x = 0.05 to 3.4+ for x = 0.2, inducing a decrease of the oxygen vacancies and favouring a random distribution over a Pm (3) over barm cubic symmetry. All the samples present an antiferromagnetic behaviour with a G-type (k = 0) magnetic structure. The increase of the Sb content induces the weakening of the crystal field (Delta(cf)) in the octahedral environment promoting the Co spin-transition from the intermediate-spin to the high-spin configuration, as evidenced by the decrease of the octahedral distortion, increment of the unit-cell volume and enhancement of the ordered magnetic moment.