Zigbee or Z-Wave for 20 door sensors in a 1950s house with plaster walls Hardware

Practical differences that matter more than range once you own twenty of them:

• Zigbee sensors are mostly coin cell, Z-Wave sensors are more often AA or AAA. Twenty coin cells a year is an annoying errand, and coin cells behave badly in the cold.
• Zigbee device support across brands is broader and cheaper, but quality varies wildly and some cheap ones report state unreliably.
• Z-Wave devices are certified so behaviour is more predictable, and the network is chattier about diagnostics.
• Zigbee pairing is faster and less fiddly in my experience, which matters when you are doing twenty in an afternoon.

None of that overturns the price argument, it just tells you where the ongoing cost lands.

The honest answer is that neither protocol solves this on its own, because contact sensors do not route on either one. They are sleepy end devices. Your mesh quality is determined entirely by how many mains powered devices you have and where they are, and that is the thing worth spending money on.

With that said, the physics is real. Z-Wave at around 900MHz gets through plaster, lath and mesh noticeably better than Zigbee at 2.4GHz, and it does not compete with your wifi. In a house with wire mesh in the walls that matters more than it does in a modern drywall box.

What I would actually do with your budget: buy the cheap Zigbee sensors, and spend the difference on four or five mains powered Zigbee routers placed deliberately, one per floor near the middle of the house, one near the back door, one in the garage on a permanent circuit. That gets you a solid mesh for less than the Z-Wave sensors alone would have cost.

The exception is the garage. 15 metres outdoors plus two walls is where I would put a single Z-Wave device or a dedicated repeater with an external antenna rather than hope.

If you go Zigbee, do the channel planning before you pair anything. Pick your Zigbee channel first, set your wifi to the non overlapping partner, and only then start adding devices. Changing the Zigbee channel later usually means repairing sleepy devices one by one, which with twenty sensors is a genuinely bad evening.

One thing to weigh that is not technical: resale of parts and availability. Cheap Zigbee sensors are effectively disposable and easy to replace in three years. Some Z-Wave sensors are less easy to source later. If you are the type to keep a system for a decade, having a common cheap part matters.

Start with five sensors in your worst locations before you buy twenty of anything. Whichever protocol you pick, the honest test is a sensor on the garage door and a sensor in the far upstairs corner, sitting there for a fortnight. That answers the question for your specific walls better than any general argument will.