I build both, so I have no reason to push one over the other. The right answer depends on what the site actually has to do.
When WordPress is the right call
Content is the point. Brochure sites, blogs, portfolios, local businesses, anything where somebody needs to add a page or a post without calling a developer.
Budget is limited. A large part of the work already exists. You are configuring more than building.
You need standard features fast. Contact forms, galleries, bookings, basic shops. Mature plugins cover them.
Somebody else may maintain it. Millions of developers know WordPress. You are not locked to one person.
When a custom build wins
The logic is the product. Dashboards, quoting engines, multi-tenant systems, anything with roles, workflows and rules. Bending WordPress into an application is possible and usually regrettable.
Performance matters. A purpose-built application loads what it needs and nothing else. No plugin stack, no theme overhead.
Security is critical. Fewer moving parts, no third-party plugin surface, and you control the update cycle.
You need real integrations. Payments, CRMs, internal APIs. Doing this properly in a framework is straightforward; doing it through plugins is fragile.
You expect to keep building. If the site is version one of something bigger, start on foundations that hold weight.
The honest trade-offs
WordPress is cheaper to start and cheaper to staff, but you inherit a plugin update treadmill and a performance ceiling. Custom costs more up front and depends on having a developer who documents properly, but it does exactly what you need and nothing you do not.
The middle path most clients end up on
A custom application for the part that matters, with a proper admin panel so the client edits their own content. That is how I usually build with Laravel — the client gets the control of a CMS on the pages that need it, and the site is not carrying a plugin ecosystem it never uses.
The question to ask yourself
Is this a website with some features, or a piece of software that happens to have pages? Answer that honestly and the choice makes itself.