Here are some comparison pics of these two side by side. If you are trying to decide between the two, maybe this will help. This isn't really a head to head comparison, these are actually different tools.
Side by side:
Ratchet Rake attachment:
Piranha Tooth Bar attachment:
The ratchet rake is an excellent tool for clearing brush, weeds, vines, etc... If clearing vegetation, making paths or light leveling are your jobs the ratchet rake is the tool for you. With the bucket at different angles, it really rips the vegetation out by the roots. As you can see, you can not dig with it. I have created several piles of rocks and dirt with the landscape rake and they are almost impossible to bite into with the plain bucket. I added the Piranha tooth bar to help with the digging duties. It can still deal with vegetation to a certain extent, but its attachment method and flat bottom make it better moving and leveling the dirt.
You may decide that one of these two, or even a more conventional tooth bar would work for you best. For me it is the ratchet rake and Piranha tooth bar.