The possible gains could be as much as 20% increase in fuel mileage due to the higher energy in diesel and the higher ratio of air to fuel for diesel (14:1 for gas and 20:1 for diesel).
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The difference in the energy content in a litre of Diesel fuel over the same volume of gasoline has been widely overblown and mis-stated. Diesel fuel does have a higher heating value by volume, but not by much (about 5%).
Also, the stoichiometric air-fuel ratio is almost identical for both fuels, both being around 14.6:1 +/- 0.1 due to differences in composition by region and season.
Diesels get most of their economy advantage by a higher compression ratio, unthrottled operation, and running lean mixtures.
A spark-ignited oil engine, while maybe giving you the benefit of multiple-fuel capability, throws away most of any advantage it has, especially when running on anything but the original fuel for which it was designed. On top of that, you add the complexity of an ignition system.
And by the way, compression ignition engines are practically by definition more "multi-fuel-capable" than spark ignited engines. With little or no modifications, you can already run a conventional Diesel engine with Diesel fuel, Biodiesel, vegetable oil, kerosene, jet fuel, camp fuel (naphtha), and most anything else that will burn. The only requirement is for the fuel to be self-ignitable at the temperatures reached in the cylinders at the end of compression.