There are a few possible issues here. But overall the answer is: things will get better, wasm perf now is not near the target.
First, asm.js in firefox has code caching. Wasm does not have that, intentionally, as there are plans to add a better and standardized way to cache. But right now it means slower warm loads in firefox.
Second, chrome on asm.js and wasm does more AOT style compilation, which is slower than the lazy approach it would use on normal JS, and is still being optimized. In particular, last I checked it was not compiling in parallel yet. When that arrives it should be a big speedup, like it was for firefox.
Another possibility is some startup changes in wasm vs asm.js code on the emscripten side. For example we need to download the wasm binary before loading the rest of the JS. If the rest of the JS is big, that might be noticeable. We should optimize that eventually. Using the browser perf tools might show if this is the issue (you'll see a pause before compiling the wasm).
Aside from those factors, if you still see wasm 1.5x slower than asm.js, then that is surprising and not a known issue in either browser - it should be faster as a binary is being loaded, no JS is being parsed. Worth creating a testcase and filing an issue.