The honest comparison is not strategist versus agency. It is judgment versus capacity.
An agency gives you people, which is genuinely useful when the work is large, parallel and needs producing — a campaign across six channels, a rebrand with deadlines stacked on each other. What it cannot reliably give you is one experienced person thinking about your business continuously, because the person who sold you the work is usually not the person doing it, and the person doing it changes.
A sole practitioner is the opposite trade. Less capacity, no team to scale into, and one senior person on the actual problem from the first conversation to the last. Nothing is translated through an account layer. Nothing is relearned when staff move on.
Which is right depends on what you are short of. If you already know what you want to say and need it made, hire capacity. If you do not yet know what you want to say — and most companies asking this question do not — capacity will produce a great deal of confident work in the wrong direction.
Worth asking in the first call: who will actually do this, will they still be here in six months, and what will you tell me when you think I am wrong.