Each frame of a 60Hz game spans 16.66ms, while in a 30Hz game it's 33.33ms. Depending on how well the engine is coded, there will be at least one frame of latency between input and reactions, and maybe more. So we could be looking at the difference between 33 and 66 milliseconds of input latency, at least. This doesn't even consider latency from input to the computer, or from the computer to the display.
Now consider that we react to events within about 200-300ms. 66ms of latency on top is going slow things down considerably, and when games are poorly coded and dump a few additional frames on top - which could happen because of propagation through events and subsystems, network latency, or animation concerns - the control starts to feel "wrong" in a hard-to-identify way.
One of the interesting things that can happen if you v-sync a game that's capped to 60FPS on a screen which has a refresh rate that is not a multiple of 60 (e.g. 70 or 100, etc) is the addition of mouse lag to the game (there's an added delay between moving the mouse and actually seeing the action happen on the screen).
And yet, like he says, Rage looks better than most 30hz games.
Before flat screens were affordable we were all using CRTs. A good CRT could push a 150Hz refresh rate. When Quake3 was still being played competitively (it /kind/ of still is with QuakeLive, but it's not the same anymore imo) we ran the game at a capped 120 FPS, set the monitor refresh to 120Hz and then turned on V-sync which equated to the smoothest and most responsive experience I've ever had in a game - it's pretty much indescribable and most people would argue that you wouldn't be able to tell the difference anyway, but even though solid 60 FPS on a v-synced 60Hz screen in most modern games comes pretty close, you can definitely feel the difference.
The worst is when you have some FPS lag with v-sync enabled - then it's a lot more noticeable than without v-sync.
I remember that during Quake4's (the 60FPS cap was hardcoded in Quake4, and somehow part of the engine, which in theory at least, made 120FPS/120Hz redundent) short run on the comeptitive scene, players complained that they wanted the cap lifted from 60FPS to 120FPS (or just any configurable number) so they could play on 120Hz monitors. id finally caved and released a patch which allowed this, and this made a huge difference. It definitely gave you an edge over the 60/60 players.
That v-sync mouse lag I mentioned has only ever happened to me when I'm using an LCD rather than CRT - which is the main reason why I wouldn't use v-sync when playing an FPS.
The scary thing is that they weren't always bullshitting about that.
Also, as sister reply said, going at 60 means no screen tearing on -anything-. Don't need to vsync, or anything nasty. TVs, computer monitors, projectors, cellphones, whatever, one whole new frame per refresh. yum.