Observed high multiplicity planetary systems are often tightly packed. Numerical studies indicate that such systems are susceptible to dynamical instabilities. Dynamical instabilities in close-in tightly packed systems, similar to those found in abundance by Kepler, often lead to planet-planet collisions. For sub-Neptunes, the dominant type of observed exoplanets, the planetary mass is concentrated in a rocky core, but the volume is dominated by a low-density gaseous envelope. For these, using the traditional `sticky-sphere' assumption is questionable. Using both N-body integration and smoothed-particle hydrodynamics, we have simulated sub-Neptune collisions for a wide range in realistic kinematic properties such as impact parameters ($b^{\prime}$) and impact velocities ($v_{\rm{im}}$) to study the possible outcomes in detail. We find that the majority ($\sim 76\%$) of the collisions with kinematic properties similar to what is expected from dynamical instabilities in multiplanet systems may not lead to mergers of sub-Neptunes. Instead, the sub-Neptunes separate from each other, often with significant atmosphere loss. When mergers do occur, they can involve significant mass loss even from the core and can sometimes lead to complete disruption of one or both planets. Sub-Neptunes merge or disrupt if $b^{\prime}Comment: 15 pages, 7 figures, submitted to the Astrophysical Journal; comments welcome