For the most part diesel will be cheaper to run on a ute or big SUV, especially when towing.
A simple rule that runs mostly true is if you can get the same fuel consumption from a petrol and a diesel vehicle the petrol will be cheaper to run.
Typically for the same fuel consumption a diesel with have more torque and probably more power, often a petrol engine in a ute will have considerably worse fuel consumption to get the same performance.
When you add in towing it seems like petrol fuel consumption will go up 50-100% depending on load/terrain where as a diesel is more like + 10-40%.
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