The question is: outperformed in what way? Level speed? At what altitude? Climb performance? At what (density) altitude? Range? Just look at how the P-51 became a great escort fighter with the Merlin, but was a perfectly fine ground attack fighter with the Allison engine. It depends on what you want to do with your airframe. It's been a while since I read it but
Jeffrey Quill's 'Spitfire' details the many development steps the type went through and includes some bits about the concurrent Merlin development.