Context. Observations of the Galactic bulge suggest that the disk formed through secular evolution rather than gas dissipation and/or mergers, as previously believed. This would imply very similar chemistry in the disk and bulge. Some elements, such as the alpha-elements, are well studied in the bulge, but others like the neutron-capture elements are much less well explored. Stellar mass and metallicity are factors that affect the neutron-capture process. Due to this, the enrichment of the ISM and the abundance of neutron-capture elements vary with time, making them suitable probes for Galactic chemical evolution. Aims. In this work, we make a differential comparison of neutron-capture element abundances determined in the local disk(s) and the bulge, focusing on minimising possible systematic effects in the analysis, with the aim of finding possible differences/similarities between the populations. Methods. Abundances are determined for Zr, La, Ce, and Eu in 45 bulge giants and 291 local disk giants, from high-resolution optical spectra. The abundances are determined by fitting synthetic spectra using the SME-code. The disk sample is separated into thin- and thick-disk components using a combination of abundances and kinematics. Results. We find flat Zr, La, and Ce trends in the bulge, with a similar to 0.1 dex higher La abundance compared with the disk, possibly indicating a higher s-process contribution for La in the bulge. [Eu/Fe] decreases with increasing [Fe/H], with a plateau at around [Fe/H] similar to -0.4, pointing at similar enrichment to alpha-elements in all populations. Conclusions. We find that the r-process dominated the neutron-capture production at early times both in the disks and bulge. Further, [La/Eu] ratios for the bulge are systematically higher than for the thick disk, pointing to either a) a different amount of SN II or b) a different contribution of the s-process in the two populations. Considering [(La+Ce)/Zr], the bulge and the thick disk follow each other closely, suggesting a similar ratio of high-to-low-mass asymptotic giant branch stars.