Agreed with people above.
I have played with games with fps ranging from 5 fps (very close to unplayable, grants you an ability to teleport from place to place, even if the game doesn't have that skill programed) to 60 fps (extremely smooth graphic)
I can assure you 20 fps will not be satisfactory. 30 fps or above is where you want it.
Computer fps is determined by many things, as opposed to that of television's; things like particles on the screen, program running in the background, material texture, shadow, object rendered, or special effects can all cause a spike or lag on your frame, sometimes even freeze.
Television, on the other hand, only needs to display the signals sent to them. Computer NEEDS to generates the signal first (in case of gaming, multiple things spontaneously) before sending it to the monitor, big difference.
How come a gaming console cost so much less than a gaming computer for the same result? No idea. Maybe that's because gaming console is built solely toward gaming, maybe computers aren't the type of machine for gaming to begin with, maybe it's because computer can do so much more, or maybe like the author said, computer company is trying to squish our little wallet.
But one thing I know for sure, having a $500~$800 homebuilt computer will definitely be worth better than gaming consoles, unless you only plans to play games and games only on the computer, then I am not sure.