That depends on the exact hardware that is configured. So it can change every day depending on what they offer.
And it could well be that a custom built mix (say, the fastest motherboard offered by Alienware and the fastest graphic card offered by Asus) is even a few procent faster.
And it might be that it depends on the game. I mean: game A is faster on the best Alienware and game B is faster on the best Asus.
And it might depend on some random choice of hardware. I mean, overclocking isn't guaranteed, but there can be a subtle difference between two processors of exactly the same model of CPU so the one you bought might be stable up to 10% overclocking, while the one your friend bought is stable up to 12% overclocking.
Why not buy both (money is no object) and start benchmarking with your favorite games?
There seems to be a lot of conflicting information out there about THE BEST gaming laptop money can buy.
Is it the Alienware 18 series (with top modifications) or is it an Asus laptop with top modifications? Are there any other laptops that you can recommend?
And by the best, I mean fastest processor, best graphics card etc. I'm not too fussed about how heavy it is or what it looks like...displaying a pretty picture is everything