Both drum and disk suffer from slipping from dust and water, but disk recover faster and are better brakes.
If both on road and off road vehicle, be sure if ABS there is a way to turn ABS off when off road. Also be sure full brakes with ABS off, some systems fail to half brakes. Nothing but trouble off road.
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"If you want to get somewhere else, you must run at least twice as fast as that!"
Disc brakes have exposed parts for the dust to get into, but as far as I was aware drum breaks also suffer from the same problem (and others). There was a group developing a sealed oil-filled drum brake years ago (because of performance loss in wet conditions), but I think that was because ABS had yet to be invented.
My vote is to stick with disc brakes like the rest of us unless it's a really special application.
Drum and disc brakes will heat up as hard usage increases. If a drum heats and expands, it will move the drum further from the friction surface. If a disc is heated, it will move the friction surface closes. Which do you want when you have pushed that vehicle too hard? Dust and dirt is about even in each. How hard are you pushing this thing? What is on the vehicle now?