The effects of chemical pressure on the structural and magnetic properties of the triple perovskite Ba3NiSb2O9 are investigated by substituting Sr2+ ions for Ba2+ ions. Two Ba(3-x)SrxNiSb(2)O(9) phases could be stabilized via a solid-state reaction at ambient pressure (AP) in air. The 6H with Sb2O9 pairs (x = 0) -> 6H with NiSbO9 pairs (x = 0.5) -> 3C (cubic with corner-sharing octahedral, x = 1.25) sequence of structural phases occurs with increasing Sr content, i.e., chemical pressure, which is like that previously reported for pure samples of Ba3NiSb2O9 obtained under increasing high physical pressure (HP). For the 6H Ba2.5Sr0.5NiSb2O9 (x = 0.5) phase, using combined Rietveld refinements of powder x-ray and neutron diffraction patterns, precession electron diffraction tomography data collected on thin crystals, aberration-corrected high-angle annular dark field scanning transmission electron microscopy coupled to energy dispersive x-ray spectroscopy mapping, we reach the conclusion that the structure features corner-sharing SbO6 octahedra and NiSbO9 pairs of face-shared octahedra (or Ni-Sb dumbbells) with either a random orientation of the Ni-Sb dumbbells or nanosized chemical correlations for the dumbbell arrangement. As observed in HP Ba3NiSb2O9 produced through synthesis at 9 GPa, AP Ba1.75Sr1.25NiSb2O9 (x = 1.25) crystallizes in a 3C double perovskite A2BB'O6 cubic structure where A, B, and B' sites are occupied by (Ba + Sr), Sb, and (2/3Ni + 1/3Sb) atoms, respectively. The B' sites, which are randomly occupied by spin-1 Ni2+ and diamagnetic Sb5+, form a face-centered-cubic (FCC) sublattice where the Ni2+ amount stays above the site percolation threshold. Weiss temperatures (eta -65 and ti -213 K for Ba2.5Sr0.5NiSb2O9 and Ba1.75Sr1.25NiSb2O9, respectively) indicate that dominant magnetic interactions between Ni2+ spins are antiferromagnetic with magnitudes like those observed in the corresponding HP phases of pure Ba3NiSb2O9. As for the 6H HP Ba3NiSb2O9 compound, in 6H Ba2.5Sr0.5NiSb2O9, muon spin relaxation (mu SR) measurements identify a dynamic magnetic state down to the base temperature (95 mK), consistent with a previously published inelastic neutron scattering study. For 3C Ba1.75Sr1.25NiSb2O9, mu SR and 121Sb nuclear magnetic resonance measurements both indicate the presence of a transition to a static magnetic state below 11(1) K with a significant amount of disorder in this frozen state, in contrast to the spin-liquid state previously suggested for the 3C HP phase of Ba3NiSb2O9. Consistently, a broad maximum is observed in the specific heat at the same temperature. Building on the structural data, the magnetic properties of HP 6H Ba3NiSb2O9 and AP 6H Ba2.5Sr0.5NiSb2O9 are discussed in light of recent works on triangular and J(1) -J(2) honeycomb systems with or without quenched disorder. We are led to the conclusion that the driving force toward a spin-liquid-like state is quenched disorder which needs to be incorporated in J(1) -J(2) honeycomb models. Our evidence of a magnetic transition to a frozen magnetic ground state for the AP Sr-doped 3C phase is in line with models for geometrically frustrated FCC antiferromagnets. This calls for a better experimental and possibly theoretical understanding of the HP 3C phase.