The short answer
WordPress is easier to set up on your own and easier to edit without a developer. Next.js is faster and has less to attack, but someone has to build it for you.
Speed
Next.js builds pages ahead of time and sends the browser only what it needs, so there is no database query between a visitor and the page. WordPress assembles the page on request, and every plugin adds to that work. You can make a WordPress site fast with caching, but you have to keep doing it. With Next.js it is the default.
Search
Both can rank. Next.js makes the right setup easier: pages exist as finished HTML, so a crawler reads them without waiting, and titles, descriptions and structured data are written in code rather than scattered across plugin settings.
Security
WordPress gets attacked more because it is everywhere and because plugins are written by thousands of different people. A Next.js site has no login page, no database and no plugin folder, so there is far less surface to go after.
What it costs over time
WordPress is cheaper to start and keeps costing: paid plugins, a developer when an update breaks something, and someone to apply security patches. A custom site costs more up front and close to nothing to keep running.
Pick WordPress when
Several people who do not write code need to publish and edit every day, like a news site or a busy blog. That is what it is built for, and it is genuinely good at it.
Pick Next.js when
The site is your shopfront: a handful of pages that must load fast, rank, and not fall over. That is most business sites.
We build every site with Next.js, including this one. The stack page lists exactly what runs it.