Sorry, this is extremly selfmade [censored][censored][censored][censored]. I hope my english is enough to say why:
The Söchting Oxydator's stand ceramics is split the hydrogen peroxide's oxygen to a atomic level. This is never reached with selfmade Oxydators. This is the reason, why this Oxydators do alot more as 100% oxygen in water.
Really, this tool is a blessing for shrimp tanks.
I don't want to get into a chemistry argument with a person who does not speak English as his primary language, that wouldn't quite seem fair, but I don't think you are quite correct on your explanation. H202 will decompose into "atomic oxygen" and water spontaneously. I have shown the decomposition reaction below. This reaction takes place on its own without an external force or additional chemicals needed to drive it.
2 H2O2 --> 2 H2O + O2
It is a fairly slow reaction though and may not release as much oxygen as you would like into your tank. This is where the ceramic comes in as it acts as a catalyst to speed the reaction up so more oxygen is released. The ceramic is probably Manganese Dioxide based and allows a faster breakdown of the hydrogen peroxide into oxygen and water. The lead weights in the linked homemade reactor are providing the same service as the ceramic, though...they are acting as a catalyst to speed up the reaction. Now the Oxydator clearly looks a lot nicer and I am sure quite a bit of studying has gone in to figure out optimal catalyst levels to give adequate formation of oxygen (without producing too much), but functionally there is no difference between what the homemade system and the Oxydator is doing. Certainly, there is no difference in the "type" of oxygen being formed, both are forming atomic oxygen (as well as water).
~Jorge_Burrito, Ph.D. (in Chemistry)
P.S. Sorry for all the people whose eyes just glossed over reading that, bad claims of chemistry is a pet peeve.
Also those snails are pretty awesome looking.