In the last band I DI'd from my X3 Live into the PA and ran an out from the X3 to my PJB Suitcase for monitoring purposes. All my sounds being generated by the X3.
The band I'm in now I play doublebass so no effects but I DI from my preamp pedal to the PA and amp in the same way.
Three main benefits, one is that I can turn up or down my volume as needed without altering the front of house mix, two, I can put my monitor amp wherever I need it facing forwards, back or sideways, whichever suits my needs at the venue, and three, less stuff to carry and set up.
No real downside for me at all.