ChatGPT is IMO a heavily fine-tuned Curie sized model (same price via API + less cognitive capacity than even text davinci-003) so it would make sense that a heavily fine-tuned Davinci sized model would yield similar results to GPT-4.
I'd expect that by now we would enjoy similar speeds but this hasn't yet happened.
If they still haven't implemented these, it would be positively surprising (to me) to see the model run at similar speeds as chatgpt now. It'd be a great achievement if they really packed such performance on similar architecture (say by just training longer)
If you have chatGPT Plus you can choose "Legacy" from the drop-down to get the smarter (and slower) 175B Parameter version of GPT-3.5. That version is the same speed as GPT-4 when load is low (early morning EST), which lends credence to the theory that GPT-4 is the same size as overparametrized GPT-3.