Or if you travel a lot ignore them and buy a laptop.
Have to agree with this. As much as i like desktops, you just can't always take them with you, specially if your visiting your family and they don't have good computers or on trip somewhere. But if your buying a laptop just to game at home... better get a desktop. But your question for Lenovo vs Alienware, Depends on specs of the laptop. Lenovo has some awsome specs on some laptops far cheaper than Alienware.
For example:
Lenovo IdeaPad Y510p
Intel Core i7 4700MQ(2.40GHz)
8GB Memory 1TB HDD 8GB Hybrid SSHD SSD
2 x NVIDIA GeForce GT 750M (SLI)
1920 x 1080
Windows 8
total: $1,063.99
:notice:
http://www.newegg.com/Product/Product.aspx?Item=N82E16834313584
DELL Alienware 14
Intel Core i7 4700MQ(2.40GHz)
8GB Memory 750GB HDD
NVIDIA GeForce GT 750M
1920 x 1080
Windows 8
Slot-Loading 8x SuperMulti Drive (DVD/R/RW)
Total: $1,249.99
:notice:
http://www.newegg.com/Product/Product.aspx?Item=N82E16834300150
So as you can see with Lenovo you get two GT 750's in sli and 1TB HDD hybrid SSD while in Alienware you just get one GT750 and 750GB HDD and on top of that it's 186$ more expensive.
Ofcorse there is other laptops with similar or better specs for the price, than those two. I would prefer this
MSI GE Series GE60, While it will have hard time beating Lenovo with two sli 750s but cosidering MSI's price 743.99$ It's a bragin. It will defenetly beat the Alienware 14.
Intel Core i5 3230M(2.60GHz)
8GB Memory 750GB HDD
NVIDIA GeForce GTX 660M
1920 x 1080
Windows 7 Home Premium 64-Bit
BD-ROM
total: 743.99$
:notice:
http://www.newegg.com/Product/Product.aspx?Item=N82E16834152393R