The optimistic model
State is published as correct by default. Anyone can submit a fraud proof during a challenge window, typically seven days, and incorrect state is rolled back. Nobody needs to do anything if everything is honest, which keeps costs low.
The cost is that a native withdrawal to Ethereum must wait out the window, because until it closes the state is not final.
The validity-proof model
Each batch is accompanied by a cryptographic proof that the state transition was executed correctly. Ethereum verifies the proof, so there is nothing to challenge and no waiting period beyond proof generation and verification.
The cost is computational: generating proofs is expensive and historically made full compatibility with the Ethereum virtual machine hard, though that gap has narrowed considerably.
What you actually notice
Day-to-day fees are broadly similar, because both are dominated by the cost of posting data to Ethereum rather than by their proving model.
Withdrawal is where they diverge: days on an optimistic rollup versus hours or less on a validity rollup. Third-party fast bridges exist for both and charge a liquidity spread to front you the funds.
Choosing between them
If you move funds back to mainnet frequently, the withdrawal latency matters. If you mostly transact within the rollup ecosystem, it rarely does, and liquidity depth for your pairs is the better criterion.
FBT Swap supports both kinds — Arbitrum, Base and Optimism on the optimistic side, zkSync Era, Scroll and Linea on the validity side — and quotes on whichever you select.