How do worn/used beyblade parts perform in comparison to newer/new beyblade parts? I'm assuming due to more use, a used beyblade part would perform less efficiently compared to newer/new ones but how differently do they perform? And at what point should you replace the parts?

Depends, In MFB Tips like WORN OUT WD worked better, In Burst worn Variable is suppose to work better than new?

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Parts like Flügel and Survive wear down to become aggressive, but Destroy and Jaggy wear down to be less aggressive, so it depends on the part.