Used a 4 side by side with my 3 in the Apple store and iOS navigation is identical. The 4 is no smoother or faster in swiping between pages and menus, etc.
The true power of the A6X will not be seen until games are updated and new titles utilise that extra power. The iPad 3 will no doubt continue to run games at 1440 x 1080 with AA like Galaxy on Fire 2 HD and NFS Most Wanted, fine by me.
As I said elsewhere though, the nature of iOS development (gaming wise) has proven that due to older devices being supported (3GS is STILL catered for on the iPhone platform) it takes a little more time for the latest device/chip to peak.
Look at Infinity Blade II on iPhone 4 and 4S. That game was supposed to be the 4S showpiece, but other than a smoother frame rate and some "God ray" lighting effects, both versions looked identical to the naked eye. Fast forward to now, a year later, and compare the recent releases like NFS Most Wanted on the 4 and 4S and the difference is night and day in terms of visual effects.
In basic iOS navigation though, other than stock apps opening a half second or so sooner, there's zero difference. iOS 7 though will no doubt change things on that count.
What I don't get is that the some of the very same people who slate those who moan about not having "the latest and greatest" turn into condescending, elitist, placebo ridden fools the second they get the latest and greatest themselves.
End of the day, there's people out there without homes, power, and loved ones due to a superstorm and we're here debating the frame rate of a tablet.