Will Claude Take over ChatGPT?

I would say it is unlikely, they don't have the same brand recognition or access to consumer devices.

In this regard, OpenAI has the strongest brand, Google and Microsoft have the best integrations in search and office products, and whoever Apple chooses for Siri will get a big bump (likely OpenAI aiui)

The marginal difference is not going to noticeably change user choice. Claude is also slower w.r.t. request response times and more expensive. Responsiveness and price will drive user choice more than the result quality

Also, that you perceive Claude to have superior results is (1) anecdotal and (2) always changing

No. With LLMs it's like with ML - if you start with usage and development of a ML product, you have to decide what framework. Once decided and build upon, it's not a easy task to change the framework. Like with Nvidias CUDA.. if you start to use it, you won't stop to use it. It's to much work and very much incompatibilities to change it .

The same applies for openAI's and the other LLMs.

It's not easy to change the LLM once it's used. May be one can have a pipeline where a joint can be switched, bit that comes on own costs and debt.

So.. no. There must be some significant change like Claude becomes Claudia and an AGI that can do a lot. Then the pain is less than the gain.