Day Rate vs Project Rate: Which Should I Charge?

A client wants a quote and you are stuck on whether to charge by the day or for the whole job. Tell it your industry, experience, current day rate, the project and how long it should take, and it compares the two models for that specific gig: where the risk sits, which fits the work, and how to convert one into the other without short-changing yourself.

I'm a freelancer in {industry} with {years_experience} years of experience. I've been charging a day rate of {current_day_rate} but a client has asked me to quote for a {project_description} project that will take roughly {estimated_days} days.

Compare day rate vs project rate pricing for this scenario. Cover:
1. The financial risk and upside of each model
2. Which suits this type of project and client
3. How to convert my day rate to a project rate with a buffer
4. Red flags that should push me toward one or the other

Give me a clear recommendation with a worked example showing the numbers.