No, they're not getting close. Top performing Wasm runtimes (like those in V8 and JSC) are generally between 10% (for pure math workloads) and 2x (conservatively, for ef allocation heavy ones) the speed of equivalent native implementations. But that's including the JIT compilation tiers; the performance of interpreters alone lags by an order of magnitude.
Between 10% and 100% ? Am I understanding that right?
I put that poorly: read as 110% and 200%
Surely you mean the "time spent," not the "speed" - as an interpreter would have an overhead, not magically speed up WASM execution. Somewhat related note, we need better tools for PGO within native compiled programs.