Wasm is stack based too. The way data flow is encoded is not so important. A compiler can easily generate code for either a stack machine or a register machine. The VM will decode that into SSA again, so it only matters insofar as the representation has to be compact and fast to decode.

The main difference is that the JVM has a garbage collected heap and high level instructions for OOP, whereas wasm is lower level than C and only slightly higher level than assembly. Instead of an object model with GC you have raw pointers.