They are similar but not the same, for instance SSE has movemask, but NEON does not, so it gets emulated(slowly) when targeting that platform. The cross lane ops are different enough that you might need to rewrite for other platforms. And then you run into situations where an instruction is very fast on one architecture but horribly slow on another because its basically emulated.
This isn't really relevant to wasm, though. You can't expect it to support platform-specific hacks just for SIMD, so you'll have to make do with the lowest common denominator anyway.