A homepage introduces the whole company. It has a menu, several services and a dozen directions a visitor can take, which is right for someone who is exploring. A landing page does the opposite: it is built for one audience, one offer and one action, such as booking a call, requesting a quote, signing up or buying. The landing page vs website question usually comes down to whether the visitor arrived with a specific promise already in mind.
If you pay for the click, the answer is almost always a dedicated page. Ad traffic sent to a homepage lands among links that pull people away from the offer they clicked on. Landing pages also make sense for a new service launch, a seasonal promotion such as Black Friday or back-to-school, an event with a deadline, or an audience that differs from the one your main site speaks to.