The pressure of knowing your 'opponent' can hear everything you do precipitates a battle over who can handle themselves the best in such a situation. It ultimately reflects your confidence and ability to take a shit.
While of course a cubicle duel is never discussed, certain rules can always be assumed:
1. Squeltchy farts, pebbledashing etc count against you - they simply reflect an inability to handle that Prawn Madras you had at lunch.
2. Splashback is essentially an own goal.
3. Bottling it, i.e. failing to lay anything down at all, results in instant disqualification - if you can't handle the pressure, get out of the kitchen (or shitter, as the case may be)
Cubicle duels can happen in any location, but are most likely to occur in the toilets at work, as most people don't have a cubicle-based shitting arrangement at home. When you're in a pub or club you rarely care, plus the ambient noise often drowns out the sound of detonating a 20 megaton monster fudge dragon.
This can add an extra dimension to the cubicle duel as you may know your opponent: seeing your enemy's face after you've beaten them can allow you to feel superior for the rest of the day, while having to look your defeater in the face can be hugely humiliating and may call for a half day.
Your internal monologue: "Right, I've got a cubicle duel on my hands here. Must...not...make...embarassing...noises..."
Your anus: "Sqeak!"
Your internal monologue: "Fuck!"