Well, I'll start with the environmental stuff. Biodiesel is made from plants, making it 'carbon neutral'. This means the CO2 it releases when it burns is equal to the amount the plants it's made of absorb when they're alive. This means it is not making any new CO2, so it doesn't contribute to the greenhouse effect/global warming. Also, we mix biodiesel with petrol/diesel for fuel (there is a certain amount legally that has to be biodiesel) and this means we are not burning fossil fuels, which, as well as being in short supply, increase the amount of greenhouse gases in the air.
As for the financial side of things. Crude oil has to be heated to extremely high temperatures to separate the fractions of oil in fractional distillation. This is when the substances have different boiling points, and can be separated by boiling and condensing. Anyway, you have to use huge amounts of electricity to produce petrol from crude oil, whereas biodiesel is organic and doesn't need to be separated.
I'm sure there are some more reasons, but this is just a start. Hope this helps x
