Web/Cloud Session vs. Local Desktop for a Multi-Hour Migration

Your team needs to run an autonomous, multi-hour database schema migration script generation and validation task — Claude will explore the schema, generate migration scripts, run them against a scratch database, and iterate on failures, mostly unattended, for several hours.

Compare running this as (a) a Claude Code on the web (--cloud) session versus (b) a local Desktop or CLI session left running on someone's machine, across three dimensions: trust/permission posture, tolerance for interruption, and cost. Recommend one and justify it.