I can say there is not noticeable difference between the two when it comes to signal strength and wireless performance when transferring between two wireless devices.
But concerning the spec. there is one serious gotcha with the Express, it has no Gb Port. The WAN and LAN ports are both 10/100Mbps ports. This means that if you have a 300Mbps Wireless connection to the Airport Express your real access to the network will be limited by the wired connection.
This can have a negative impact on large file transfers and Time Machine backups.
The power supply of the Express is built-in while with the extreme you need to make room for the power supply where it will be installed.
Subjectively the Express seems to be slightly better at dispatching WiFi through the floor bellow it.