The solver produce different results as they are different solver using different numerics and primitive variables.
In both methods the velocity field is gained from the momentum equations. In the density-based approach, the continuity equation is used to obtain the density field while the pressure field is determined from the equation of state.On the other hand, in the pressure-based approach, the pressure field is extracted by solving a pressure or pressure correction equation which is obtained by manipulating continuity and momentum equations.
The pressure-based solver traditionally has been used for incompressible and weak compressible flows. The density-based approach, on the other hand, was originally designed for high-speed compressible flows. But now both can be used for almost all flows.
You need to tell us more about the models and numerics used in each solver. Seems like the PBS solution is suffering from some wiggles.
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