I preferred Personal Computer because i played 10-15 hours straight a day when i am still a gamer,so my Laptop would be burned if i use it that long and the battery wont be enough.
But now?i only use Mobile or Ipad because my game is simpler and can be played using smaller gadgets.
Laptops that will be used for longer hours will absorb heat because of being compress. While in desktops, there's enough space for the temperature to be regulated inside the system unit. I have used laptops in gaming before but I'm not confident on it and still use desktops for it.
Life of desktops is longer than laptops but it still varies to the user how he will take care of both.
I would personally go for alienware without a doubt. Stability is number one when it comes to gaming laptop so better get this one.
If this par with my budget, I have actually bought my very own Alienware.