We explore the multimessenger signatures of encounters between two neutron stars (ns(2)) and between a neutron star and a stellar mass black hole (nsbh). We focus on the differences between gravitational-wave-driven binary mergers and dynamical collisions that occur, for example, in globular clusters. Our discussion is based on Newtonian hydrodynamics simulations that incorporate a nuclear equation of state and a multiflavour neutrino treatment. For both types of encounters we compare the gravitational wave and neutrino emission properties. We also calculate the rates at which nearly unbound mass is delivered back to the central remnant in a ballistic-fallback-plus-viscous-disc model and we analyse the properties of the dynamically ejected matter. Last but not least we address the electromagnetic transients that accompany each type of encounter. We find that dynamical collisions are at least as promising as binary mergers for producing (short) gamma-ray bursts, but they also share the same possible caveats in terms of baryonic pollution. All encounter remnants produce peak neutrino luminosities of at least similar to 10(53) erg s(-1), some of the collision cases exceed this value by more than an order of magnitude. The canonical ns(2) merger case ejects more than 1 per cent of a solar mass of extremely neutron-rich (Y-e similar to 0.03) material, an amount that is consistent with double neutron star mergers being a major source of r-process in the galaxy. nsbh collisions eject very large amounts of matter (similar to 0.15 M-circle dot) which seriously constrains their admissible occurrence rates. The compact object collision rate (sum of ns(2) and nsbh) must therefore be less, likely much less, than 10 per cent of the ns(2) merger rate. The radioactively decaying ejecta produce optical-ultraviolet 'macronova' which, for the canonical merger case, peak after similar to 0.4 d with a luminosity of similar to 5 x 10(41) erg s(-1). ns(2) (nsbh) collisions reach up to two (four) times larger peak luminosities. The dynamic ejecta deposit a kinetic energy comparable to a supernova in the ambient medium. The canonical merger case releases approximately 2 x 10(50) erg, the most extreme (but likely rare) cases deposit kinetic energies of up to 10(52) erg. The deceleration of this mildly relativistic material by the ambient medium produces long lasting radio flares. A canonical ns(2) merger at the detection horizon of advanced LIGO/Virgo produces a radio flare that peaks on a time-scale of 1 yr with a flux of similar to 0.1 mJy at 1.4 GHz. Collisions eject more material at higher velocities and therefore produce brighter and longer lasting flares.