I use copilot cli and I can pick Anthropic models. The Microsoft interface seems fine to me, and equivalent. Not sure what the big deal is.
Funny I had the opposite experience. The Claude models seemed equivalent to GPT-5.4/5 in a generic harness like Copilot CLI or Opencode or Pi, but Claude Code the app/harness is so much better than all the others that I switched at work, even though I'd much prefer to use a non-proprietary harness (and eventually I do want to get Pi set up to be comparable).
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Harness makes a difference. Also in copilot you have smaller context for Claude models.
And you get a token based pricing since June 1.
Anthropic's Claude harness is much better than Copilot, i.e. the tools and instructions in each harness are different. Anthropic is just that much better (for claude models, likely an amount of co-development).
Personally, I looked into Copilot's prompt and saw things that made me put it down immediately to start working on my own. I'm now using OpenCode for reasons and I like it better than any Big Ai tool. Using OC with Qwen3.6-MoE (for context) and generally happy with the results.