Having played in brass bands for donkeys years street marches have a steady tempo and it is quite usual to switch from 6/8 to 4/4 and vice versa.I would say if the 6/8 is not slow and is played as two beats to the bar then in 4/4 keep the main beat the same ie 4 beats to the bar so in foot tapping terms 2 taps in the 6/8 and 4 taps in the 4/4 at the same tempo