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We investigate the effects of nonequilibrium dynamics in small colliding systems by comparing a nonequilibrium transport approach, the Parton-Hadron-String-Dynamics (PHSD), with a (2+1)D viscous hydrodynamic model, VISHNew. Focusing on p+Pb collisions at LHC energy, we extract the initial conditions for the hydrodynamic model from PHSD, in order to reduce the impact of the early out-of-equilibrium dynamics and focus on the traces of nonequilibiurm in the ensuing medium evolution. We find that in the transport approach quantities like energy density and bulk viscous pressure are highly inhomogeneous on the transverse plane during the whole evolution, whereas the hydrodynamic simulations dissolve more efficiently the initial spatial irregularities, still keeping a high degree of inhomogeneity due to the smaller size and lifetime of the medium produced in p+Pb collisions with respect to heavy-ion reactions. As a first step that will help to identify the impact of these nonequilibrium effects on final observables in proton-nucleus collisions, we perform an analysis of the transverse spherocity, an event-shape observable able to distinguish between jetty and isotropic configurations of transverse momenta. We found that the spherocity distribution in PHSD is slightly shifted towards the isotropic limit with respect to the hydrodynamic result. Even though this dissimilarity is partially due to the difference in the final charged particle production, it mainly comes from the different description within the two frameworks of the medium produced in small colliding systems. This finding supports the idea that multi-differential measurements, such as those based on event categorization according to multiplicity and spherocity, are useful to study final-state observables in ultrarelativistic proton-nucleus collisions.