The question comes up in almost every first meeting. It is a fair question, and the honest answer is not one of the two names. It is a third thing: how long can you wait, and does your site currently turn visitors into enquiries.
One rents, the other accumulates
Advertising is visibility you rent. You pay, you appear at the top today, and the day you stop paying you disappear. That is not a flaw; it is what the channel is for. It is the fastest way to test a market, a message or a new product.
Search visibility accumulates. It moves slowly at the start and it keeps returning after the work stops. It is also harder to take away, because it rests on pages and trust rather than on a daily budget.
Advertising buys today. Search buys tomorrow.
The better question
Before choosing a channel, look at what the site already receives. If a hundred people arrive each week and none of them write, adding a thousand more will produce ten times nothing. The first job is the page, not the channel.
The second thing to settle is the wait. If you need enquiries this quarter, advertising is the only honest answer. If you are building something you expect to sell for years, search is where the compounding is, and starting it late costs the most.
A practical order
For most companies the sequence looks the same. Make the site convert what it already gets. Connect conversion tracking so spend becomes readable. Run a narrow, well measured campaign on the terms closest to purchase. Then use what those campaigns reveal about real queries to decide where the search work goes.
Done in that order, advertising pays for itself sooner and the search work is aimed at terms you already know convert. Done in the other order, you spend twice to learn the same thing.
If you want to look at which of these your own situation calls for, we can go through the numbers you already have.