the flat pedals are on my mountain bike, so I don't have experience riding flats in the wet. where I live, riding trails is 100% unacceptable when it's wet—very sticky mud leaves nasty ruts and cakes onto your bike like concrete. if the trails are wet, I ride my CX bike on roads and gravel paths to avoid the mud and I use SPD pedals and shoes for that.
IME, trail running shoes with large lugs SUCK for flat pedals because the pins don't consistently bite the sole. I much prefer something with a relatively flat, even sole similar to a skate shoe. however, most skate shoes get shredded to ribbons very quickly on pedals with protruding pins, so I don't waste money on shoes like that.