I'd have thought there would be little CPU performance difference (it's the same JavaScript code after all), and either none or a small improvement on GPU performance (since it can issue frames off the main thread). So I wouldn't expect any huge changes - the main benefit is it runs off the main thread so browser work on the main thread won't jank the game.
Still it's worth verifying this with performance measurements - and for those, just use the same ones as ever, there's nothing special about performance measurement in worker mode. E.g. measure the FPS, CPU utilisation, GPU utilisation, etc.