Probably the most common way to charge a project is by the hour. Often the rate decreases as the hours increases. Usually to give a more competitive price and also because they save time. The downside to this method is that cost can exceed your budget if the time required increased. This is a bad approach for uncertain projects.
Why do some projects cost more even if the duration is the same? Some projects require strenuous effort, more risk or addition cost to the freelancer. This cost would be factored into the rate they charge.
So you think you can hire someone for 10 minutes and pay much less? Tough luck! Some will reject without a beat, some might impose a minimum time, some will simply start at a much higher rate than they usually would when working for many hours.
Having a fixed amount both parties agreed on can be a benefit to everyone. Or not. When a fixed price is given, the freelancer would not charge more or less than stipulated. This means that if the project overruns the estimated time, the freelancer loses money. On the other hand, if the project completes early, the freelancer get all the profit. The advantage to this approach is the predictable cost.
Break Down Cost
Big project can be very expensive. Feel free to ask the freelancer for a break down of the cost to see where all the money is going. They should be able to provide this easily because they should have done the break down when estimating the cost.
Which Do I Choose?
Well, you don't really get to choose since each freelancer has their own preferred method. But if you don't like taking risk, go for the fixed amount.