Quad: one machine each
Choose the quad when everybody wants their own machine and the point of the outing is the riding. It is the most physical of the three and the dustiest. Beginners are fine — the briefing covers everything you need.
Buggy: two seats, shared drive
Choose the buggy when you would rather sit together. It is more stable, it protects you better from the dust, and it lets a nervous passenger enjoy the terrain without having to pilot anything.
Camel: walking pace
Choose the camel when the landscape matters more than the activity. It requires nothing of you, it makes no noise, and at sunset it gives you the photographs everyone else wishes they had.
Or take two of them
The most popular half day in the collection is the quad and camel pairing precisely because groups rarely agree. You get the engine first and the walking pace afterwards, with a tea stop between.