The 60D and T4i/T5i have sensors that are (virtually) identical, so if you're shooting RAW, there will be no difference in image quality. The main reason to get the 60D would be better build quality, ergonomics, and a more sophisticated autofocus system. Personally, I shot with the Rebel series for eight years and never felt compelled to upgrade, at least in a chasing environment. It may be a case where you don't miss those extras until you've actually been using them.
Throwing the Nikon in makes it tricky. On the one hand, Nikon's D5x00 series is rather cheaply-made -- they're even more stripped down and plasticky-feeling than Canon's Rebels. But at the same time, the sensor in the D5200 is better than Canon's by a margin that can be quite noticeable in some situations. If you shoot RAW and are willing to spend time processing your photos in Photoshop (or similar software), the D5200 will give you more to work with than any of the Canon bodies.
Have you considered the Nikon D7000? It was basically the direct competitor to the Canon 60D, and should be around the same price. It gives you a great sensor and much better build quality than the D5200.
Are you planning to use a DSLR mainly for stills, or will video be a major consideration? If so, Skip is correct in that Magic Lantern might make Canon the better choice.