After switching to Sony, I find it much easier to salvage photos taken in high contrast situation, vs my T3i. I can expose to preserve highlights, then pull the shadows an still get clean photos. With T3i, the shadows were always an issue in harsh light. There's no denying Canon's DR is nowhere near what Exmore can produce.
But there's more to camera than just sensor. I briefly tried D5200 and I hated nearly everything about it, despite the great sensor performance. If I ever go back to a DSLR, it would be Sony or Canon (not going to spend the money on D800). Canon strong points are sharpness (where D5200 fell short), ruggedness, good customer service, pleasing colors, plenty of relatively cheap good lenses, great controls. Sony has sensor performance, focus peaking (good feature not only for manual lenses), EVF (which I really came to like as it gives WYSIWYG picture), and in their large cameras also IBIS.
Canon is a leading camera company. They make their own sensor (unlike Nikon) and while this is very beneficial from a business perspective, this also means they can't quickly adapt their manufacturing processes. It's not that they can't design a sensor with better DR or high ISO performance, likely it can't be produced on their current tooling and it is too expensive to retool.