Fundamentals
Snapshot vs onchain voting

It is rarely either/or. Mature DAOs signal offchain and settle onchain.
Cost and participation
Offchain voting is free and lifts turnout dramatically. Onchain voting costs gas and filters out casual voters.
Authority
Only an onchain vote can authorise an onchain transaction without a trusted human in the middle.
The hybrid pattern
Temperature-check offchain, then run a binding onchain vote on the exact payload that will execute.