I, on the other hand, have a 7D, a camera that isn't that old in tech comparison.
2009 is ancient in "tech comparison". The 7D has many good features but it also has an old sensor and processors.
I have both. Key differences (that I can think of off the top of my head) are:
Controls, of which there are pros and cons. Joystick is very nice on the 5D3. Play button has a silly location on the 5D3 and is easily accessible with the shooting thumb on the 6D. Depth of field preview button is small and harder to find on 6D for some silly reason.
Dual cards. Great if you can't afford to loose a shot, as in weddings, events. etc. Otherwise you can back up regularly using wifi on the 6D. Another point is the 6D can make full use of UHS SD cards, the 5D3 can use them, but not at their full speed. Not sure that's a big deal.
FPS - do you need 6 fps, or is 4.5 fps enough?
Focus - another mixed bag. The center point on the 6D has the best low light performance of any camera anywhere at this moment
. The other points are pretty useless for tracking and very low light. Disabling all but the center point in AI Servo improves things. 5D3 seems complicated but the AF system is relatively easy to learn. I don't think the AF on the 6D is as bad as most people who've never used one make it out to be, but there are limitations. Canon really screwed the pooch by not at making all sensors cross type. Despite the sensitivity of the 6D's center point, this is a clear win for the 5D3.
High ISO performance - slight edge to 6D.
Overall image quality - slight edge to 6D as well.
In camera HDR - 5D3 will save the RAW files for you if you set it that way. 6D will only give you the resulting jpeg. Same with multiple exposures. Of course you can do your own HDR with your own RAW files using the 6D and any HDR software.
Custom shooting modes - two on 6D, three on 5D3.
Custom file names on 5D3, not on 6D.
Weight - the 6D is lighter and easier to carry all day.
Wifi and GPS - if you use them they're nice. Wifi app and capabilities could use some work.
Video - you don't shoot now (neither do I except occasionally with my phone) but this is a clear win for the 5D3 in several ways, and may factor into resale value down the road.
Cost - as you've pointed out, they are very different in cost. Clear win for the 6D.
Shutter durability rating, max sync speed, and max shutter speed differences are all mostly red herrings designed to distinguish one from another. All are slight edges for the 5D3 but even in sum are hardly meaningful.
I'm sure there are a few bells and whistles that I've forgotten, but that's a lot of it.
I live in a resort city where there's a lot of street entertainment at night. I got a lot of use out of my 6D at night this summer and really enjoyed it.
If you want to shoot a lot of fast moving birds, land animals, sports, etc, the 5D3 is superior, but all that can
be done with the 6D. Of course you might miss some shots. You may get more keepers with the 5D3, but some of the keepers from the 6D may be "better".
If you're really torn, consider renting each, one after the other, and seeing which you like, and whether the 6D can perform for you. Taking a few snaps in a camera shop is not going to answer that question really. Either one will be a step up in image quality from what you are using now.
Edit - another point - "silent mode" is really close to silent on the 6D, on the 5D3 not as much.