Some games/platforms like to market their graphical quality, and some like to instead talk about frame rates. In a perfect world we'd have both. Hardcore PC owners can even buy 120Hz gaming monitors.
But does it matter? Not always. But if you've ever played a driving game that requires quick reflexes (i.e. open world driving games with lots of traffic to avoid - Midnight Club 3 was a shocker for me personally), if you can quickly switch between 30 and 60FPS while driving, I really do notice a big difference, and driving with precision becomes a lot more easier and enjoyable. If you've got a PC capable of 60FPS a good way to test switching between 60 and 30 is to setup FRAPS to record at 30FPS.
For those who've not given it much thought before, this German gaming website has published a short video that compares 20 FPS, 30FPS, and 60FPS. Watch it a couple of times and see what you think.
http://www.pcgameshardware.de/LCD-Hardware-154105/Specials/Die-besten-Monitore-LCD-Tests-Bestenliste-1074792/