Though these methods have inherent detection strengths and weaknesses, in my experience the materials usually determine which NDE method is used. Typically, magnetic particle is preferred when the base metals can be readily magnetized. I believe the simplest reasoning has to do with the fact that liquid penetrant inspections are more time consuming due to required "dry" and "dwell" times.
Another consideration is that "dry magnetic particle testing" can be performed on hot metal, which is obviously advantageous in the scenario of "NDE every pass". With wet MPI and LPI, liquids would quench a weld that hasn't sufficiently cooled, making the process much more time consuming in your scenario.
Generally, in terms of sensitivity, these methods are comparable. That said, there are several different kinds of MPI and LPI to consider as well, if increased sensitivity is required.