I'll try to actually answer your quick "?" with a relevant answer.
I have a quick question about the dynamic range of the 5D3..what am I missing out on? ..
Not a lot, under most conditions.
I always shoot JPEG with highlight tone priority enabled and do my best to get the exposure and WB spot on. I also shoot in Faithful picture mode with the contrast turned down one notch. I end up with pretty flat images out of the camera with plenty of details in the highlights and shadows. Unless I really mis the exposure I have never been unhappy with the DR.
considering that you're not shooting raw, and your typical subject matter, your approach is a reasonable and practical one that's working for you.
It'll take more effort, card memory and time to post process raw files to extract a little more from them under the harsher lighting conditions where it may benefit some shots.
However, shooting raw and more PP work would likely give you more of an improvement than shooting jpg on a D800. Then again, Nikon's active D-Lighting can work quite nicely on jpg only output too so also worth considering; you may prefer how it would impact your current workflow.
High end cameras like the 5D3 and D800 do a pretty good job of fitting the DR of the scene into a fairly pleasing jpg output. Altho they both do pretty a similar job, they do it slightly differently so each camera's jpg output of the same scene will look a little different and there'll also be a wide variation on each body's rendering of the shot depending on all those jpeg-relevant options you select in each camera.
If you have the opportunity, you should try shooting some test shots alongside your usual method using a D800 and trying some of its settings to see how it changes the jpeg output. You could also try a D7000 or even a D5100 as they all have similarly high DR at base ISO and more than Canon's.
I remember reading someone recently posting on one of CR's forums here how much better he thought the D800 did in hi contrast, sunlight sitations where he was able to not only recover nice luminance information, from people's faces in a mix of sunlight and shade on one face, but that there was more COLOR and detail information to be had from the D800 in this situation too. He claimed this was the difference between selling a shot or not. He posted an example but honestly I can't confirm that this would be correct since I didn't buy a 5D3 and I don't know how long I still have to wait for my D800. Considering that the shadow area adjacent to a sunlight area on the same surface is only a few stops difference at most I can't see the 5D3 having any trouble accomplishing the same thing.
The greater color information, extractable from the darker areas, CAN be better with the D800 than with most of Canon's cameras because of the lack of noise in the D800's shadows compared to the Canon's. Canon's dark noise tends to include a lot of red channel noise; when shadows are boosted you may have to subdue it by reducing some color saturation in the shadow areas which can yeild a less pleasing image. You typically have to push very dark areas very far before this is a problem and the 5D3 did make some slight improvements in this area over the 5D2 so it's even more pushable than the old 5D2.
So, should you buy a D800 based on this kind of shooting?... Probably not. but it might be worth a try anyway just to see if you prefer the kind of output you get from it. Many people have also said they prefer Canon's rendition of skin tones over Nikons and I might agree a bit there too. I've generally always preferred the "look" of a Canon image which is why I also use DPP to do most of my raw file image processing.
It's probably a better first step to shoot raw with your 5D3 and see what you can do with it in post. Under very contrasty conditions, yet not so bright as mid day, I'd also opt to turn off the HTP as it won't help your raw files and can actually hinder shadow recovery. Process with DPP (or LR4) for ease of tweaking.
I've converted a few long time and very experienced jpeg event shooters into raw shooters after they saw how much more they could do with that raw file!
I am not trying to start another debate over the two cameras I just want to know how much better it is and how much of a difference it would really make.
You seem to have unleashed another round of that argument, but that's a good thing. I'm glad more Canonites are discussing this issue and more are getting a good grasp of it while some are still steadfastly unconvinced. That latter group is likely to see the dark one of these days.. and it won't have reddish banding in it.
Aw heck, if they haven't seen the red noise lurking in the shadows yet they're just not pushing the limits of their gear.
I hope I've been able to answer some of your question.