One possible advantage of WeatherBridge over MeteoBridge is that (if Ambient does its job; and I am pretty sure they do) ensures you will not receive a TP-LINK device that is not supported. Other than that, MeteoBridge is equivalent and buying HW yourself and licensing MB is lots cheaper (and is what I have done over 2 years ago). It should not be that hard to buy a correct version of hardware.
Once you have it setup, these issues do not exist, so the Ambient benefit mentioned above is marginal.
Having said all that, it is quite unfair to blame MeteoBridge for incompatible HW versions in TP-LINK. It is TP-LINK that releases substantially different hardware under (mostly) the exact same product name/version. Of course TP-LINK never sells these devices with MB in mind, but rather sells them as a self-contained router. As such the changes should not, and do not, matter. I also suspect this is one of the reasons why Boris introduced MB PRO, because it gives complete hardware control. It is, however, substantially more expensive and does not necessarily offer much additional value (depending on your needs) beyond basic intermediary between your weather station and various services.