Arkaan's comments are 100% correct, but since I've recently been shopping for a gaming laptop myself I thought I'd add a few things.
First, for a gaming machine (as Arkaan said) the most important things to consider are the GPU and CPU. RAM also matters a little, but 8GB (which most laptops will have) should be plenty unless you're doing non-gaming stuff with the machine like serious Photoshop or programming.
CPU is easy to figure out: you just want higher numbers. Let's say you're going Intel: you want an i7 over an i5 if possible, and then within the i7s there are various ghz, and you want the highest you can get (although really the exact amount of ghz isn't
that important, so don't sweat that as much).
Graphics cards are trickier though, because there are so many of them out there. Luckily this page takes all the work out of understanding them for you:
http://www.notebookcheck.net/Compari...rds.130.0.html
It has every card you might want to consider ordered by power, so all you have to do is just get the highest one on the list that you can afford.
One last thing to consider: hard drive speed. Hard drive's basically come in three flavors these days: 5400rpm, 7200rom, and SSD. This won't affect your gaming as much, but it will matter for how fast your computer can start up, and how fast you can read/write data to your hard drive, so if possible you want an SSD, and if not a 7200rpm one.
Next up, if you want to get the most bang for your buck, you'll want to find a deal. I do this in two ways: first, I check sites like Amazon.com, Newegg.com, and TigerDirect.com every day or so, looking for deals. Second (and this is the more important one if you really want a good deal) I check Techbargains.com daily. That site finds all sorts of coupons and deals, and using it can literally save you hundreds of dollars.
Oh, I also check Google Shopping, but be careful: there are scam companies that list on there, and they'll try to get you to do sketchy things like pay for your computer using an Amazon gift card. So, while you might find a legit deal there, just be skeptical, and if a too-good-to-be-true deal doesn't seem to be legit, it probably isn't.
As for the two computers you mentioned, they are fairly similar, and both have the exact same graphics card. But if you look carefully and follow what I said you'll notice that the Asus has ...
- a 7200rpm hard drive (vs. the Lenovo's 5400rpm)
- an i7 CPU (vs. the Lenovo's i5); the Asus actually has slightly less ghz, but as I said the ghz don't matter as much as the CPU type
- 16GB of RAM (vs. the Lenovo's 8GB); as I said 8GB is probably all you'll need, but that 16GB might come in handy someday
So the Asus seems like the winner to me. But before you pick either one, I'd strongly recommend checking the sites I mentioned (especially Techbargains.com) for a few days, and compare what you find to the Asus. You might even want to create a spreadsheet (I did).
Hope that helps.
P.S. Oh, I almost forgot: weight. Personally I consider tech specs more important, but depending on how much you plan to carry the laptop around weight might actually be a bigger issue for you.