A landing page does one job: get a single visitor to take a single action, like booking a call or buying one product. It's focused, fast to build, and easy to test. A full website does many jobs: it explains who you are, lists services, hosts a blog, and serves visitors at different stages.
If you're launching one offer, running an ad campaign, or validating an idea, a landing page is usually the smart first step. You learn quickly and spend little.
If you need a lasting presence that multiple types of visitors return to, a full website earns its cost over time. It's harder to outgrow and gives you room to add sections as you grow.
Many businesses don't have to choose forever. A common path is to start with a strong landing page, prove the offer works, then expand it into a full site once the direction is clear.