I used to think that cameras handled highlights differently. I actually still think that to a small degree, they do, and in some ways I think Canon cameras do handle highlights better. I definitely no longer think that there is nearly as much headroom in the highlights as reported by the camera itself as I used to think, though.
When I say the 5D III burns highlights, I mean that highlights go from "good", with nicely separated tones, to "poor", where things are all just blended together mush, and often a near-blown-white creamy color...VERY FAST. There isn't any room up there...you go from good clean highlights that are eminently recoverable, to not fully blown, but not really usable either, in a heartbeat. There are only a few levels at the upper end of the linear range where your highlights aren't blown, but where they seem to bleed into each other across color channels. When I first got my 5D III, I ETTRed with it the same way I did with the 7D, and it simply did not handle that the same way.
That's different from the 7D. The 7D seems to have a lot of highlight headroom. I've overexposed shots with the 7D by a couple of stops, and was able to recover quite nicely in the end, without any actually blown highlights. I could ETTR quite far with my 7D, and sometimes I'd clip highlights, but it wasn't that often that they became an unusable creamy-white blur before that point.
Now, this is based off of what the camera reports. I've long been an ETTR fiend...it's kind of the only way to use Canon cameras. If you don't push the exposures in-camera, your losing a lot of usable DR, because the read noise is higher than with Exmor sensors. The way the 7D reports the highlight clipping point, you can still expose for about a stop or so before you actually clip the highlights in RAW. I guess it's just a difference in how Canon generates the JPEGS, but I find that I barely have the ability to expose a third to two-thirds of a stop with the 5D III before the highlights get to the point of unusability, and usually at that point they clip as well. Same meter, in both cameras...so it has to be a difference in how the JPEGs are generated.
Anyway, even when shooting in manual mode, you ultimately determine your exposures based on the in-camera histograms (generated from JPEG), in-camera highlight warning (generated from JPEG), and in-viewfinder metered/exposure compensation scale. The scale seems to be based directly off the meter, however you never quite know how the tones will distribute in the image until it's taken. So in the end, you base the "properness" of your exposure off the in-camera histogram. That histogram, at least base off of my own experience with my own 5D III, is unforgiving of highlight overexposure. When you do ETTR...the 5D III tends to "burn" the highlights...since there really isn't much room there.
I suspect the 5D III was updated to simply be more accurate. That's a good thing, but when you have spent years with a particular camera that behaved a particular way, you tend to base your experiences off of the thing you have the most experience with. My 7D, being quite forgiving with highlights, is my reference point.
My limited experience with the D800 seems to indicate much the same. It seems their highlights just kind of ride up to the top, then suddenly they clip. There isn't the same kind of headroom as the 7D. Again, that's probably just the camera being more accurate, when it tells you the highlights are clipped, it usually really means it. The difference with the D800 is...you simply don't NEED to ETTR. Not nearly like you do with Canon cameras. You still can, but it's just not a necessity. Two years ago, I'd never done more than hold a D800 for a few minutes in a store, so, I did not have any real depth of understanding about how it's data is really distributed. I also had delusions about how good the 5D III was...truly, delusions.

It's really NOT as good as thought it was back then, not from a low ISO DR standpoint anyway.