Aeotec sells a z-wave range extender, but doesn’t every non-battery powered z-wave device do this? So, why would I buy this over, let’s say, a Fobaro wall plug?
It not only repeat, it amplifies signals 
Almost every mains powered Z-Wave device behaves in exactly the same way as the Aeotec repeater. In fact, the repeater shows up in Vera as a binary switch, complete with a non-functional On/Off button.
Some people choose the Aotec repeater for it’s lower cost, when they do not need a plugin relay. Some people like it because it is smaller and has a less noticeable appearance. Some people choose it because they believe that it has a better signal or different characteristics than a plugin appliance module, which it does not.
For me, I’d rather spend a few extra dollars and get the added benefit of a switchable relay, such as with the GE 12719 Z-Wave Wireless Lighting Control and Appliance Module. But some people would rather not spend the extra ~$5.
Thanks for the responses.
As for the French blog, very interesting read.
For those not fluent in French, it concludes that a wall plug does the same thing as the Aeotec Range Extender, but the Aeotec device is very good a what it does and extends the range pretty far (further than the tested wall plug). The writer does however find the Range Extender overpriced for it’s functionality.
(the test is obviously more extensive than this summary)