Just one of the many articles that are slowly surfacing, now that WebAssembly is interesting enough as possible attack vector.
While there is a sandbox, you can attack WASM modules the same way as a traditional process via OS IPC, by misusing the public API in a way that corrupts internal memory state (linear memory accesses aren't bound checked), thus fooling future calls to follow execution paths that they shouldn't. With enough luck, one gets an execution path that e.g. validates an invalid credential as good.
The JVM implemented properly should not have security issues. The class library however... (i.e. it's a lot easier to sandbox things if you start without any classes that interact outside the sandbox).
The JVM is fairly good at sandboxing, as these things go. Turns out sandboxing arbitrary software is an extremely hard problem (as the WASM folks are starting to encounter in the wild)
At least in so far as the higher level (DOM, browser runtime) and lower level (memory access, to the extent that it's mediated by the WASM VM) have no security issues...
The VM itself is pretty tight, but abstractions have a nasty habit of being leaky.