Ethernet Cable vs Wireless adaptor
Thunderbolt Adapter

Pros


Cheaper
No software configuration
Faster (although depending on the speed of the internet connection, this may be less of a factor)
More reliable (no interference, etc.)


Cons


Only usable with Macs with Thunderbolt
Mac is physically tethered to the cable
Sharing connection with other devices requires leaving the Mac on all the time


Airport Express

Pros


Works with any device that has Wi-Fi
Multiple devices can be connected at once, without additional setup
Allows your device to be free of wires


Cons


More expensive
Requires some configuration
Requires an additional power outlet
More gear to keep track of
Subject to interference from other Wi-Fi networks


If all you need to do is connect to a wired network, the Thunderbolt Adapter is probably the way to go. It's really no different than plugging into a dedicated ethernet port on older machines.

You should really only consider the Airport if you definitely need wireless capability or other devices need access when the Mac may not be available. Your Mac can create its own hotspot to share the ethernet connection with other devices, (like an iPhone).