tldr: Given an option, A dedicated AP with a management backend is likely to have better features and functionality. A mesh router is good for larger areas where you can't really lay out wired backhaul. A repurposed router in AP mode, or with DHCP functionality turned off and the port in the lan part of the router is the cheapest option.
A good mesh device is an AP, that uses a dedicated/separate wireless (or wired) backhaul to communicate between APs. The secret sauce in most cases is in the software and set up.
I find a 'regular' AP gives you more flexibility if you have a wired backhaul (and there's good 'prosumer' grade APs like the unifi models that are going to be significantly easier to manage than a repurposed consumer router)
Your mileage may vary with mesh routers. They tend to be pricer so there's not significant price savings and tend to be app controlled, which is great, when it works, but sometimes, you have issues. On the other hand, you set one up, they're preconfigured and any changes happen without the need to set up multiple devices. Its worth finding a model that does triband (using a 5ghz channel for backhaul) or ethernet. There's also a few companies (like ASUS) who have models that do both mesh functionality and regular APs. Also with a mesh router, to get full advantage of its functionality, you're constrained to units in the same ecosystem, so you can't really mix and match hardware. Wired backhaul is also uncommon, and mostly found in more premium units.