Look at price
= actual price after talking to a phone rep
And don't buy a desktop, never buy a desktop. Make your own, doesn't take long to learn, doesn't take long to do. Only reason you'd buy a desktop is for warranty, which you don't really need on a desktop tbh since it's not really going anywhere.
If you DO buy one, get it from NCIX, though.
(http://pc.ncix.com/ncixpc_new/ncixpc.cfm?uuid=09D161B3-8BAB-4E17-B5879E8F424429DD-4690112) Basically exactly the kind of computer it sounds like you're looking for, great gaming, great video editing despite adobe not currently supporting the gtx 680 for premiere pro.
To build one what DonGio said, though.
CD/DVD/BD drive (the hands/mouth) -> Asus
RAM (the attention span) -> if you want to do any sort of significant video editing, 16gb min, 8gb is fine for most people, though
Video Card [also referred to as GPU] (the eyes) ->Depends what games you want to play on max. For last chaos maybe like integrated graphics, lol. I would say if you want the most recent, Nvidia 570 or 580 on the green team, and one of the reasons for going nvidia is that their CUDA technology will help your videos a ton. Even though these are slightly older video cards, they're no slouch, prices have dropped since 600 series has come out, and they're the only non-Quadro cards that are certified by adobe premiere pro cs6, because again, I'm assuming you're doing real video editing work. If the program you're using only supports Open GL 4.1, then either grab an nvidia 660TI or amd 7970.
CPU (the brain) ->i5 is fine for RIGHT NOW in terms of gaming, because most games don't use more than 2 cores, however again for video editing I suggest minimum i7 3770. If you plan to overclock, get the 3770K
Motherboard (the vertebrate) ->Asus z77
The tower (the body) ->Make sure it's large enough to fit all the components, or small enough to fit into the space you want. The alienware is nice in this regard because it's about the size of a console, but with like 100x better graphics.
Power Supply (the lungs) -> wattage depends on other components, but get a Corsair one.
The hard drive [HDD] or solid state drive [SSD] (the memory) ->If you're building your own, there is really no excuse nowadays not to have at least a 64gb SSD boot drive. Again for video editing though, if you plan on using adobe, I might recommend at least a 128gb version, along with minimum 2TB hard drive, depending on what type of footage you're capturing.
An operating system (the personality) ->Linux.
Sorry if you were really set on one of those two, since I didn't really give you that much advice, but I can't really recommend either one of those the moment you said video editing. If I had to pick though, I'd go with the alienware, but customize it from Dell. Also note that it does have an external power supply, and it is quite beefy.