Claude Code runs long terminal sessions: explore a repo, touch many files, keep output in shell history. Cursor Composer stays in the editor: diffs, file clicks, MCP wired to the current workspace.
If you mostly issue tasks in a terminal and rarely click the file tree, Claude Code fits. If you want to accept patches beside the editor, Composer fits.
Both can load MCP and skills, but config paths differ. This site only stores metadata; follow each client home for exact files.
If unsure, run the same filesystem MCP and one development skill on a small change in both, and see which matches how you read diffs.