What are the benefits of using conservative temperature in oceanography?
The TEOS-10 manual, page 26, says that the potential temperature is the temperature that a parcel of fluid conserving its Gibbs energy and absolute salinity would have if brought to the surface, or from an integral of the adiabatic lapse rate. The conservative temperature is not a true temperature, but a multiple of the enthalpy. It's really an energy that's been scaled to have units of temperature. The scale factor is the heat capacity of water in a standard state, since it's taken to be constant. In the potential temperature, the heat capacity is allowed to vary during ascent. 

This distinction crops up a lot in meteorology, where the moist static enthalpy is conserved under adiabatic ascent, whereas other measures of temperature aren't conserved. I think the reason for the change is similar to why we would use enthalpy in meteorology, too. Suppose that the adiabatic changes in pressure and temperature also change the equilibrium coefficients of some reaction, say $\ce{CO2 + H2O -&gt; H+ + HCO3-}$. This would change the absolute salinity, since it's splitting apart a water molecule into ions. The actual ascent can be adiabatic - there's no mixing with the surrounding water - but it's no longer isohaline. The enthalpy will still be conserved, though. This is why I think your questions (here's the other one) are related: using a mass-based salinity fits in much better with a thermodynamically-consistent formulation of the Equation of State, and using the enthalpy over the potential temperature is part of this complex salinity-temperature-entropy relationship.

The manual mentions that near the surface, the differences between potential and conserved temperature should be really small. The heat capacity chosen to scale the enthalpy is similar to that for surface water. You'd get the largest differences at depth and where the composition of seawater is much different (like with absolute salinity). The difference here is whether that composition is expected to change with temperature and pressure.