I use all three (MCP/CLI/API) based on what Claude excels at:

* CLI: GitHub & AWS it already knows how to operate the CLIs well. Even learned about a few new CLIs like 1Password's op which it volunteered one day.

* MCP: Supabase, Shopify etc. where the CLI would be non-obvious and the affordances from the tools/descriptions helps Claude maneuver.

* API: Sometimes it just knows an API exists and is able to call it directly with python/curl. I discovered from Claude the Pokemon ecosystem has a free API out there for example.