Which gaming computer is the better choice?

I don't know

Build the desktop. Gaming laptops are almost always bad if you buy them under 1 grand.

If you buy a laptop that that can be used for many purpose, it is more profit since both of them has same cost.

You know you can just go to Microcenter and buy the components to build your own tower for a fraction of the price of a pre-built machine, but that's probably not an option if you're not handy with PCs. Lenovo makes laptops, lets see the specs are…
Intel Core i7 (4th Gen) 4700MQ / 2.4 GHz quad core
8 GB RAM ddr3
1 TB HDD / 5400 rpm
14" 1600x900 display.
NVIDIA GeForce GT 755M - 2 GB GDDR5 SDRAM,

It's okay for the price, but you really would want to upgrade the Ram to 16gb minimum for gaming in my opinion.
I don't like gaming laptops, so i would definitely look into purchasing a desktop, but that would require you purchasing a good 120hz monitor, wireless adapter, mouse, and keyboard and since i don't know your budget i can't say for sure.

Build a desktop

Toshiba or HP are better choice for gaming.