Both routes get a page live today. The difference appears when something changes, and it compounds.

What each produces
Prompting produces a file. Open it in any editor, publish it anywhere, hand it to a developer, keep it forever, regenerate it from a prompt when it needs rebuilding.
A builder produces a design inside the product. There is no file. The page exists because their software renders it, on their infrastructure, under their terms.
That is the whole comparison, and every other difference follows from it.
| Prompted | Built | |
|---|---|---|
| You hold a file | Yes | No |
| Publishable anywhere | Yes | No |
| Editable without the tool | Yes | No |
| Guardrails | None | Real |
| Survives the product closing | Yes | No |
| Non-technical daily edits | Awkward | Easy |
What a builder is genuinely good at
Guardrails.
It is hard to produce something broken. The mobile layout is handled. Nobody is ever looking at markup wondering why the page is blank. A person with no technical confidence gets a reasonable result in twenty minutes and never sees a console.
That is worth real money to a business where the person updating the page is not technical and does it weekly.
Dismissing builders because they lock you in misses this. The lock-in is the price of the guardrails.
What prompting is genuinely good at
Producing something specific.
A builder gives you the page its templates can express. A prompt gives you the page you described, including the calculator, the odd layout, the thing no template covers.
And it gives you the file, which means the decision is reversible in a way the builder's is not.
The question
What happens in two years.
Somebody non-technical edits it weekly. A builder. Handing them a file to edit does not work, and it will stop being updated.
It changes rarely, or you are the one changing it. Prompt it, keep the file, publish it. Regenerating from a prompt is faster than learning an editor.
You do not know. Prompt it and keep the file. That choice can become the other one later; the reverse cannot.

Keep the content either way
Whichever route, keep the text and images in a folder you own.
Then rebuilding in a different tool is a layout exercise rather than retyping from screenshots. This costs nothing at the time and it is the difference between switching being annoying and being a project.
The domain settles the rest
Put your own domain in front of whatever you choose.
Then the page can be rebuilt, the tool can be changed, and every published link keeps working. Without it, choosing a tool is choosing an address permanently.
If this is near what you are doing, Choosing a Carrd alternative and How to create a website using an assistant cover the cases on either side.
Put it at an address
Ask what happens in two years. Builder if somebody non-technical edits it often, prompting if you want the file, content in your own folder either way, and your own domain regardless.
Then the choice you make today is one you can change.