We have compared the halo kinematics traced by globular clusters (GCs) and planetary nebulae (PNe) for two elliptical galaxies in the Fornax and Virgo clusters NGC 1399 and NGC 4649, and for the merger remnant NGC 5128 (Centaurus A). We find differences in the rotational properties of the PN, red GC, and blue GC systems in all these three galaxies. NGC 1399 PNe and GCs show line of sight velocity distributions in specific regions that are significantly different, based on Kolmogorov-Smirnov tests. The PN system shows multi-spin components, with nearly opposite direction of rotation in the inner and the outer parts. The GCs velocity field is not point-symmetric in the outer regions of the galaxy, indicating that the system has not reached dynamical equilibrium yet. In NGC 4649 PNe, red and blue GCs have different rotation axes and rotational velocities. Finally, in NGC 5128 both PNe and GCs deviate from equilibrium in the outer regions of the galaxy, and in the inner regions the PN system is rotationally supported, whereas the GC system is dominated by velocity dispersion. The observed different kinematic properties, including deviations from point-symmetry, between PNe and GCs suggest that these systems are accreted at different times by the host galaxy, and the most recent accretion took place only few Gyr ago.We discuss two scenarios which may explain some of these differences: i) tidal stripping of loosely-bound GCs, and ii) multiple accretion of low luminosity and dwarf galaxies. Because these two mechanisms affect mostly the GC system, differences with the PNe kinematics can be expected.