Interestingly, asm.js has an advantage in Firefox and Chrome for me, but not in Safari.
I played 4 times on Safari with varying settings and it always converged into 50%/50% play ending in a draw.
Whereas in Firefox or Chrome sometimes even after 10-15 turns, the asm.js version had 98-100% chance of winning.
More specifically, Firefox and Edge detect "use asm" and run an asm.js type-checker, while Chrome detects "use asm" and runs TurboFan.