I don't dispite Zed is great, I actually am using it myself, but it's an editor first and foremost. The OP, to me at least seems to be asking more-so about the AI agent comparisons.
It's not only that they have it built in but it seems to be currently the best open replacement for tools like claude code cli because you can use arbitrary llm with it, ie. from ollama and you have great extension points (mcp servers, rules, slash commands etc).