I don't think moving from one SLR system to another SLR system is going to make for a big difference in size. Sure, the body may be smaller, but the lenses won't be, and they end up taking most of the bulk if you've hit the point where size is an issue. Sure, the D5300 is going to be significantly smaller, but hook it up to a decent lens, and the size difference won't be all that big. For the Nikon, I used the most comparable lens to the Canon 15-85 - the 16-85 VR, and chose an OM-D and Pen with prime lenses to compare them to (I chose 17mm 1.8 and 45mm 1.8)
So yes, the body is smaller and lighter, but a comparable lens will be comparably sized, negating the advantage.
If you like the Canon and want to stick with an SLR, you might consider one of the Rebels with a pancake lens or two - that will get the size down a lot.
The m4/3 cameras here with prime lenses will exceed the capabilities of the slow zoom lenses in general use (They also have in body image stabilization). The downside here is cost and expandability. There is a decent amount of m4/3 stuff available, but outside of the inexpensive prime lenses, they do get quite pricey. If you're concerned about DOF, the difference in DOF is a bit less than 1 stop. An f/4 lens on APS-C is equivalent to an f/3 lens on m4/3. The fast primes will get you more subject separation than an f/2.8 zoom lens will on the APS-C bodies.
If you had a more comprehensive kit, there would definitely be a bigger hurdle to making the jump, but as someone who recently rented an OMD EM1 and a couple lenses, the system really impressed me. It doesn't handle as well as the Canon does, but the size difference is astonishing and the quality is more than enough for me. So I picked up a used Pen and a couple of the little prime lenses to play with, and will be making a similar decision to you, difference being I have a backpack full of Canon kit and making the switch won't be cheap.