What special about Apple AirPort Extreme? I considering to replace my old wifi router and purchase AirPort Extreme.
Why airport extreme feature that make it price is higher than common router WIFI?

it is faster transfer data?
Better WIFI range?
etc...
Wireless is a complicated topic and you need to consult a speciality website like smallnetbuilder.com if you want to understand things like range, performance, and capabilities of different routers.

The Apple Extreme/Express are more expensive, require an Apple utility that runs only on iOS/OS X/Windows, and are not the most feature rich.  However, they are simple to use if you live in a mostly Apple world and have some unique Apple features that can be useful in that world.  For example, it's dead simple to wirelessly extend an Extreme/Express network and Apple Express routers can be hooked to speakers to use with AirPlay.

I just used three Expresses to replace an old 802.11g network (it used four old Linksys routers wirelessly extended to get about 50% coverage) at a friend's condo.  It's only a single floor with about 2500sf but the walls are all steel-reenforced concrete so wireless range was extremely limited.  It took all of about 10 minutes to install three units and network them with a single SSID and WPA password.  I would have preferred wired connections but it wasn't a practical option due to the construction.

I can't see much advantage to the Extreme over the Express with the current models unless you want to use the gIt might have better antennas and thus better performance but I think that's an edge case. It also may have some additional features so you'd need to do a feature-by-feature comparison.