My understanding is that, for example, businesses that were aryanized were sold at low but not completely nominal prices but I am not sure. I assume that in invaded countries, property was simply taken with some counterexamples as in Hungary where businesses were paid for with both money and allowing owners to leave Hungary safely at least in the case of large business owners. A broader question is how were agreements abided by once made? If businesses were sold in exchange for safe conduct, were the former owners actually allowed to leave? Why were legal formalities observed at all?
The title asks about legal protections under two different governments; the question in the body asks why legal formalities were observed. I'm not sure which question you want answered. The body of the question seem to contain a thought experiment about some hypothetical businesses being nationalized.
Fundamentally legal niceties were observed because the Nazi's perceived themselves as a legitimate state. No protection were offered to Jews because the Nazi's felt that Jews were criminals. Most governments limit the rights they accord to criminals. In most states, it is illicit for criminals to keep the profits of their crimes; by criminalizing genetics, it became entirely legal to seize the wealth of Jews, because they could only have obtained that wealth through criminal activities that weakened the state and harmed German citizens.
Part of the horror comes from criminalizing genetics. Think about that for a while and then go hug your kid.