The 60D is a mid-level body. It begins to incorporate features of the pro bodies -- control layout is more similar to the pro bodies.
From a T3i, the two most obvious differences you'll notice will be that the 9 point auto-focus system consists of ALL "cross-type" focus points (much faster and more accurate to focus as compared to your T3i which only has a single (center) cross-type point and all other AF points are single-axis only.) Also the control layout is much nicer with the selection wheel in the front (just like your Rebel) but the back of the camera has the multi-control dial both a wheel and joystick-type control built-in. It allows much faster adjustment to camera controls. There's also the top LCD with the four control buttons (AF, Drive, ISO, and metering mode -- oh... and a light). The ISO button has a bump on it since that's the most frequently accessed button -- it lets you find the button and change ISO speed without removing your eye from the viewfinder.
It's has a weather-sealed body (but you're not "really" weather sealed unless you also use weather-sealed lenses) and you'll find the body grips "feel" better (it's a more comfortable fit and the body cladding has a better rubber non-slip grip to it -- less like plastic.)
The sensor and image processor are essentially the same. The pop-up flash can work as a master to control a slave flash (e.g. the pop-up flash on a 60D can actually remotely fire a slave flash such as the Canon Speedlite 430EX II). I *think* that's also true of the T3i... but not sure. I know the T2i and older Rebels cannot control a remote slave flash unless you buy a master flash controller or flash capable of operating in master mode (such as the 580EX II).