Hm. It depends how much you care about accuracy. ChatGPT does a great job overall, but I have found frequent errors and hallucinations around numbers, names, and dates in particular.
If you do go for GPT-4, just be careful of this. Where other transcription services might fail, or give some implausible output which highlights that you need to check the source, ChatGPT might give a highly plausible but incorrect transcription from which you might not immediately identify that transcription has failed.
Ideally OP would keep the source images of the original journal pages around even after transcription. I think ChatGPT (or LLM in general) is probably the best option, but the best overall solution would accept that LLMs are flawed and would require long-term iteration.
The problem with ChatGPT is that you might not know to check the original.
If the original text is “I’m getting married on the 10th July”, you’ll know to check the handwritten note if it says “I’m getting married on the l@ July” but not necessarily if it says “on the 16th July”. ChatGPT seems to do the second quite often.