If you want a result by a certain date, onset speed is the number that matters. Cleveland Clinic says Dysport is faster, then immediately shrinks the claim.
The onset claim
Cleveland Clinic writes: "Dysport tends to kick in more quickly because of its formulation and how it spreads after injection. It uses a different protein complex than Botox, which may help it reach the targeted nerve endings faster. That said, the difference in onset is usually minimal. Both usually start working within a few days."
The direction is Dysport first. The size of the gap is "usually minimal", and both products land within a few days.
The trade that comes with it
A second Cleveland Clinic page pairs speed with duration: "As a result, Dysport may offer faster outcomes, but Botox may last longer."
Speed and hold time pull in different directions here. Both statements are hedged with "may".
What to do with a minimal gap
Do not choose a product to save a day or two. If your date is fixed, book early enough that a few days of onset on either product still lands before it.
More from Cleveland Clinic is available on the Botox Cosmetic page covering uses and side effects, its cosmetic injectables treatment overview and a piece on the long-term effects of Botox.
The careful reading
A faster start only helps if the result then lasts. Ask your provider how often you would return on each product, since repeat visits are what you keep paying for.