I'm currently looking into the Nikon D5200 but I don't feel as if I've done enough research so I tried going for a broader question to see if I should continue to look further. I actually already tried holding the D5200 & the D5300 at Target & Best Buy but idk... I just didn't like the feel of it. I'll probably get used to it, the more I hold it but I was more comfortable holding the T3i in my hands. So conflicted...
Canon T3i is a nice camera choosing it will not be a huge mistake but the Nikon D5200 is a better camera.
It has a better and more modern sensor, the sensor on the T3i is around 6 years old which means in technology world that its very old, the sensor on the D5200 is less then half its age.
It has the advantage in low light, better dynamic range and has more resolution.
The auto focus system is also much better so I do recommend the D5200 over the Canon T3i.
The D5300 is obviously a great camera and is a small upgrade from the D5200 but I am not sure the money difference is justifying the small upgrade, it depends how much of a jump in value the D5300 is from the D5200 in your store.