I had an issue with playwright MCP where only one Claude Code instance could be using it at a time, so I switched to Claude's built-in /chrome MCP.

In practice, I also find it more useful that the Chrome MCP uses my current profile since I might want Claude to look at some page I'm already logged in to.

I'm not very sophisticated here though. I mainly use use browser MCP to get around the fact that 30% of servers block agent traffic like Apple's documentation.

I was using the built-in chrome skill but it was too unreliable for me. So I switched to playwright cli and I can also have it use firefox to get help debugging browser-specific issues.