Custom GPTs live inside ChatGPT's interface — great for a person running the task manually in a chat window. Claude Skills are built to run inside an agent that's already doing file operations, running code, or orchestrating a multi-step task, which matters the moment you want automation, not just a smarter chat.
If the goal is "anyone on the team gets the same quality output for this recurring task," both work for prompt-and-context packaging. The gap shows up when the task needs actual tool use — reading files, running scripts, hitting APIs — not just better instructions.
If a human is going to run it manually in a chat window a few times a week, either works — pick whichever platform your team already lives in. If it needs to run as part of an automated pipeline with no human in the loop, that points toward the agent-based approach, not a standalone chat GPT.