If you are open to either and there isn't a particular lens from either you 'must have', then the fundamental difference is the sensor.
It's not possible to say one is better than the other. They are so very different. A few things here:
The 36MP of the D800 create big RAW files. And you'll be wanting to shoot RAW. The files are around 45MB each, the Canon is about half this. If you take a lot of images you'll need more backup drive space with the Nikon. The benefit to the Nikon at least is you'll be able to crop your images more without loss in quality if you print: you won't notice a difference when you print a 36MP image compared to a 22MP image, unless you're printing giant posters. Being able to crop like crazy might be very useful if you're starting out again as a born again photographer. I'm aware that the Nikon sensor is far superior at getting back shadow detail in post processing, the Canon is horrid. I suspect that if you underexpose your shot, you can get more back with the Nikon in post.
Critically, if you want action shots though, the D800 can only handle 4 frames per second and you'll miss a lot of shots. The Canon manages 6 frames per second, still nothing to shout about but 50% better at least. Both have fantastic autofocus systems, the Canon might tip the Nikon a little.
The built in flash on the Nikon is not there to be used as a flash so much as a 'commander' to remotely trigger external flash units. If you wanted to use it as a proper flash, then you would have to have a very small lens like a 50mm prime, and even then, the results aren't usually very good. It is however VERY USEFUL. Importantly, if you invest in some Nikon flash units like an SB-800 or SB-910, then you can use Nikon's 'CLS' system (Canon call theirs E-TTL) which in simple terms will automatically expose your subject correctly - you do not have to manually set the flash, or if you do want to, you can set the external flash power from within the camera. The 5D Mk3 can't remotely trigger flashes, and to get it you have buy expensive accessory unit. If you want to get into lighting, then the Nikon has that edge.
Lastly, go to the shop and try them out. You may find the ergonomics of one is much less suitable, or you find the layout and functionality of one more suitable.


