Your code can get messy fast when dealing with CSS3 transitions. I would recommend using a plugin such as jQuery Transit that handles the complexity of CSS3 animations/transitions.
Moreover, the plugin uses webkit-transform rather than webkit-transition, which allows for mobile devices to use hardware acceleration in order to give your web apps that native look and feel when the animations occur.
Javascript:
$("#startTransition").on("click", function()
{
if( $(".boxOne").is(":visible"))
{
$(".boxOne").transition({ x: '-100%', opacity: 0.1 }, function () { $(".boxOne").hide(); });
$(".boxTwo").css({ x: '100%' });
$(".boxTwo").show().transition({ x: '0%', opacity: 1.0 });
return;
}
$(".boxTwo").transition({ x: '-100%', opacity: 0.1 }, function () { $(".boxTwo").hide(); });
$(".boxOne").css({ x: '100%' });
$(".boxOne").show().transition({ x: '0%', opacity: 1.0 });
});
Most of the hard work of getting cross-browser compatibility is done for you as well and it works like a charm on mobile devices.