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Acknowledgements. P.S-B acknowledges support from the Ramón y Cajal program, grant ATA2010-21322-C03-02 from the Spanish Ministry of Economy and Competitiveness (MINECO). F.F.R.O. acknowledges the Mexican National Council for Science and Technology (CONACYT) for financial support under the programme Estancias Posdoctorales y Sabáticas al Extranjero para la Consolidación de Grupos de Investigación, 2010-2012. We acknowledge financial support from the research projects under grants AYA2010-21887-C04-03, AYA2010-21322-C03-03 and AYA2010-15081 by the Spanish Ministerio de Ciencia e Innovación. J. F.-B. acknowledges support from the Ramon y Cajal Program, grants AYA2010-21322-C03-02 from the Spanish Ministry of Economy and Competitiveness (MINECO). R.A.M is funded by the Spanish program of International Campues of Excellence Moncloa (CEI). C.J.W acknowledges support through the Marie Curie Career Integration Grant 303912. I.M. acknowledges financial support from the Junta de Andalucía through projects PO8-TIC- 03531 and TIC114, and the Spanish Ministry of Economy and Competitiveness (MINECO) through the project AYA2010-15169. We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr). Based on observations collected at the Centro Astronmico Hispano-Alean (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut ur Astronomie and the Instituto de Astrofsica de Andaluca (CSIC). FCT/MCTES (Portugal) and POPH/FSE (EC). He acknowledges support by the Fundação para a Ciência e a Tecnologia (FCT) under project FCOMP-01-0124-FEDER-029170 (Reference FCT PTDC/FISAST /3214/2012), funded by FCT-MEC (PIDDAC) and FEDER (COMPETE). We also thanks the referee por his/her suggestions that have improved the final version of this paper., While studies of gas-phase metallicity gradients in disc galaxies are common, very little has been done in the acquisition of stellar abundance gradients in the same regions. We present here a comparative study of the stellar metallicity and age distributions in a sample of 62 nearly face-on, spiral galaxies with and without bars, using data from the CALIFA survey. We measure the slopes of the gradients and study their relation with other properties of the galaxies. We find that the mean stellar age and metallicity gradients in the disc are shallow and negative. Furthermore, when normalized to the efective radius of the disc, the slope of the stellar population gradients does not correlate with the mass or with the morphological type of the galaxies. Contrary to this, the values of both age and metallicity at ~2.5 scale-lengths correlate with the central velocity dispersion in a similar manner to the central values of the bulges, although bulges show, on average, older ages and higher metallicities than the discs. One of the goals of the present paper is to test the theoretical prediction that non-linear coupling between the bar and the spiral arms is an efcient mechanism for producing radial migrations across significant distances within discs. The process of radial migration should flatten the stellar metallicity gradient with time and, therefore, we would expect flatter stellar metallicity gradients in barred galaxies. However, we do not find any diference in the metallicity or age gradients in galaxies with without bars.We discuss possible scenarios that can lead to this absence of diference., Spanish Ministry of Economy and Competitiveness (MINECO), Mexican National Council for Science and Technology (CONACYT), Spanish Ministerio de Ciencia e Innovación, Junta de Andalucía, Fundação para a Ciência e a Tecnologia (FCT), Depto. de Física de la Tierra y Astrofísica, Fac. de Ciencias Físicas, TRUE, pub