They use the same active ingredient (Botulinum toxin type A) and work the same way, by blocking nerve signals to muscles which relaxes movement and soften wrinkles. They differ in some of the accessory proteins used to stabilize the toxin.
Botox: The industry standard. Great precision. Takes 4-7 days to kick in.
Dysport: Spreads slightly more, making it excellent for large areas like the forehead. Kicks in faster (2–3 days).