Both claim to fix dead zones. They work very differently, and the right choice depends on your house, not just your budget.
If your dead zone is one room and budget matters, an extender is a reasonable fix. If it's a whole floor, multiple rooms, or you want one seamless network, mesh is worth the extra cost.
It can — rebroadcasting the signal typically cuts available speed roughly in half on that extended network, which matters more for heavy use like streaming or gaming than for basic browsing.
Most mesh systems are designed to replace your existing router entirely as the main unit, with additional nodes placed around the house — check the specific system's setup requirements before buying.
Generally not in a way that works well — they're different approaches to the same problem, and combining them tends to create more configuration headaches than it solves. Pick one approach for your whole home.