The question is not which form is cheaper, but who carries the risk when the work turns out harder. Under a project price that is the agency; under an hourly rate it is you.
By project, as soon as you can describe the scope
You get an amount and the agency gets the responsibility to deliver within it. If it takes longer than expected, that is their problem. Which is why a project price usually sits slightly above the sum of the estimated hours: it contains a risk margin, and you pay it knowingly.
What to settle alongside it: the number of feedback rounds, what happens on a change, and what is not included.
By the hour, only for what you cannot bound
Research, coaching, a crisis, an exploratory phase, or work whose size depends on your own decisions. Here an hourly rate is fairer than a project price, because an agency forced to name an amount for an unknown scope prices itself against the worst case.
What to settle alongside it: a ceiling per phase, and a mandatory alert when that ceiling comes into view. An hourly rate without a ceiling is an open account.
The form that works out best most often
A project price for the bounded parts and an hourly rate for the tail you cannot describe, in one contract. That is clearer than one form stretched over everything.
Where it always goes wrong
A project price on a scope that is not settled. You then negotiate every change for three months, and at the end the relationship is damaged over an amount smaller than the time the discussion cost. If you cannot describe the scope, the first assignment is that description, and the price comes after.
And one thing not to forget
An hourly rate says nothing about the price. Two agencies at the same rate can differ eightfold in hours on the same line. So compare what gets made, not what the hour costs. See what a normal hourly rate is, and the PAR instrument IKAg uses to express a proposal in units of work.
See also: which remuneration models exist and how to keep costs from running away.