wasm is more baked into the web platform than either are; flash wasn't as bad as java in this regard, but still. Nobody wrote flash libraries that your JS code could use, they used it for the equivalent of a big old <canvas>.
It also does not require a second runtime; integrating wasm support into existing JS VMs took very little code compared to an entire JVM or flash runtime.
> Nobody wrote flash libraries that your JS code could use
This isn't precisely true. Before widespread availability of similar HTML 5 features, Flash was used for file upload (especially multiple files w/ progress bars), clipboard access, and pre-websockets network push. Client-side image processing, too, although you might consider that as part of the "big old <canvas>" usage. Your overall point is right on, of course.
It also does not require a second runtime; integrating wasm support into existing JS VMs took very little code compared to an entire JVM or flash runtime.