Shot Canon (5D), moved to the D800 about a year ago now.
Lenses I can't talk about too much because the only first party lenses I've used on either have been the 50s. In terms of systems to be honest it's just a matter of getting to know them.
There were a few main reasons I went with the D800, and many of them are specific to me and won't really apply to most:
1. Resolution/Stupidly big prints - I had a fair few big pieces to do for exhibitions and the like, and 36MP vs 23MP is an appreciable difference for 50" prints.
2. IQ - While the 5D3 is certainly getting there, the D800 remains comfortably ahead of the Canon offerings particularly in dynamic range. The 5d3 is perfectly good enough if you're not exposing like a moron, but sometimes I'm a moron. I'd had to bin a fair few 5D images over the course of my using it because I didn't expose quite right (99% of the time my fault) but I've never had to drop a D800 image due to exposure problems even with a lot of mucking about with 9 stops et al.
3. Price - I'm not sure what prices are like at the moment, but at the time of making my choice the 5D was about a £600 dearer option, not to mention I could sell off my Canon gear to go a substantial way towards my D800 purchase and rebuild the system over time, and if I was going to sell off half of my lenses anyway sticking within Canon for its own sake lost its appeal.
Now, the Canon is definitely better than the Nikon for video, and while I can use the D800 perfectly well, subjectively I still prefer the Canon control layout (the control wheel in particular). In addition, I prefer Canon's lens lineup, not least because the top end stuff is generally a hell of a lot more affordable for what I shoot and 95% as good (plus available second hand) i.e. 35L, 50L, 85L, 100L, 135L. However, I'm primarily a sigma shooter nowadays so that's not mattered too much.
Another point is I really don't like the D800 battery grip method having to have one battery inside the camera and only one in the grip because it makes having two batteries really annoying. I loved shooting with a grip on the 5D but it's just too much hassle taking batteries in and out on the D800 to be worth it.
AF is meant to be better on the 5D3 but my shooting isn't really of the sort that would every highlight that sort of differences. Noticeable step up from the 5Dc I had but that's not really the topic of discussion here.
I'd say the sensor is noticeably better in the D800, while erring towards action/video favours the Canon, but there's a lot more to the decision than just dxo performance metrics. At the end of the day all (D800, D800E, 5D3) are brilliant cameras and whichever you buy, history has shown you'll be in one of these threads defending it to the death before long, so unless there's a really specialised area you want to focus/invest in then both will be able to serve you very well.
One downside would be if suddenly I couldn't get photos I want and Nikon did, as that would be an enormous reinvestment!