The dielectric properties of the solid solution Ba1-xSrxTiO3-delta ( 0 <= x <= 1) have been investigated. The nanopowders were prepared via a coprecipitation reaction followed by a calcination treatment. Spark plasma sintering allowed to obtain dense nanocrystalline ceramics. Broadband impedance spectroscopy revealed colossal permittivity (epsilon' = 10(5)) associated with low losses (tan delta = 0.03) in the most favorable case. The bulk conductivity data was analyzed using Jonscher's universal dielectric response model. In the Ba-rich compound, conduction process followed variable range hopping conduction model while the Sr-rich BST compound showed the nearest neighbor hopping conduction mechanism associated with displacements of space charges. These two different conduction mechanisms might be able to explain superior temperature-frequency-independent dielectric properties in Sr-rich BST compound compared to Ba-rich BST compound.