One company has the capacity to maintain HIPAA compliance and the other is best known for vacuuming up the entire web and users prompts. For something as sensitive as family photos, I know which company/product I'd prefer for this potential project.
Google's mission statement is to "organize the world's information", and the only thing stopping them is when they run into copyright laws or paywalls.
OpenAI (and indeed all the LLM providers) has gone almost as far as it can usefully go with bigger training sets, even without literally everything on the web, and now try to make the models smarter in other ways.
(OpenAI may also lose their current copyright lawsuits because laws don't care that both an LLM and PageRank are big matrix multiplications, they care about the impact on rights holders).
"your ancestor has this indicator of that hereditary disease, good morning your health insurance now costs you 1.5x and we don't actually have to explain why"