Basically the 15.6" laptop is smaller and lighter. If you can live with playing games on a smaller size screen but with the same resolution, then there shouldn't be a problem. The only issue you may have is that everything looks smaller.
I have had no problems switching between my desktop rig with 26" 1920x1200 monitors to a 14" laptop with only 1366x768 resolution when it comes to games.
There's little difference in the gaming experience. Let's assume both resolutions, processors, graphics cards, everything... are the same... in a 15.6 inch screen laptop and a 17.3 inch screen laptop. The difference then, is ONLY screen size. And that too, only a 1.7 inch difference, which isn't really much.
As mentioned above, the 15.6 will be a lighter laptop and easier to carry around. If you're considering getting a new laptop, don't worry so much about whether it's 15.6 or 17+ inches... look at the processor, RAM and GPU... Assuming, of course, that the laptop has a 1920x1080 res.