Do brick or stone roads last longer than asphalt or concrete roads?

That's a solid "it depends". And in this case, it depends on the definition of "lasting" and the definition of "road".

Klinkers are near immortal, but they're laid on what we call a "street layer" of 3cm of compacted, specifically graded sand, on top of some 25cm of less expensive sand. That sand can shift, compress and ruin the stability of the bricks. That usually happens due to heavyweight transport, or external factors (settlement of the soil underneath, tree roots, etc). If you run just passenger cars in a suburban area on steady ground, it could last 50 years. If you supply your stores on a road like that, it's more like 10 years. But you can remove the brick, regrade/replace the sand and rebuild it from mostly the same bricks. Concrete bricks don't last as long, and they break more when removed/packaged/relaid, I don't really know the numbers.

Asphalt is different. Assuming we're talking about a road that could also be made in bricks, asphalt has a surface layer of some 3-5cm, then between 10 and 20 cm of underlayers in layers of around 5 or 6cm. Then some 20-30cm of gravel, and up to half a meter of sand. That top layer lasts something like 10 to 15 years, and it suffers most from frost/thaw, UV light, etc. You don't have to replace al of it at once though, you can patch it.

The underlayers generally fail due to traffic weight, but that can be 2, 3 or maybe even 4 cycles of surface layer replacement later. Generally, for busier (non high-way) roads, they replace the surface layer twice and the third time they do parts of the underlayers, or all of it, depending on damage. Asphalt can be 80 or 90% recycled though, but it takes quite a bit of heat (something like 3 to 6 cubic meters of gas for each ton of asphalt).

So, all in all, not all brick roads are equal, not all asphalt is equal. And "how it lasts" is a complex question too. It's also a tough comparison, because we generally don't build roads for the same purposes. If it's very busy, we usually don't use bricks.