This is an ASUS forum so most are going to be a bit biased here.
Having just walked down the same path myself with a new rig I Once again chose the ASUS, G752Y DH72.
I also looked at Alienware.
A few things about the alienware disqualified it. Firsty that beautiful UHD display, If you have anything that will actually use its full resoluition it willl drag down its performance. The heat issue was also another problem, every reviewer had the same complaint of several places on the keyboard passing 110F. Screen briteness is a bit less and color reproduction isnt as good. Most benchmarks when ran apples for apples the two were pretty close.
The only pro I could give to the alienware is the ability to easily add their graphics amplifier which is basically an external desktop graphics card.
Neither of the two has good audio, The Asus G751 series was actually better than the G752. So if you are anything like me and want good audio be prepared to use something other than the on board speakers. For me I dont like headphones on me head or plugs in my ears so I use a Bose soundlink III over BT which isnt as good as getting a nice external PC speker solution and plugging it in but it is portable and wireless.
The battery life on the alienware may be better when you are doing simple tasks like web surfing but make no mistake about it. There isnt a portable gaming solution on the market that has good battery life, its a performance trade off. If battery life for surfing is your top priority you might want to consider a different platform like a Lenovo Thinkpad T450 with an extended battery it gets 15+ hours but suffers in the performance arena horribly.
“Two things are infinite: the universe and human stupidity, I'm not sure about the former” ~ Albert Einstein