Well, I wouldn't want to be stuck using an f4 lens at a wedding. I'd want at least an f2.8 zoom, if not an even faster prime (or set of primes). I would also be highly inclined to use flash as much as possible, since available light shots can be unattractive, badly shadowed, and fill flash can really improve a shot when used right. Of course, not all venues allow flash and it's not appropriate in some situations.
But for low light shooting of any sort, you have to consider two main things: high ISO performance of the camera and it's ability to focus in low light.
High ISO performance, if you shoot RAW it's a bit of a toss up... 5DII, 6D and 5DIII are close to the same. However, both 6D and 5DIII are settable to higher ISOs than 5DII (two stops or 102400, vs 25600). Only you can say if those higher ISOs are actually usable. They are pretty niosy, but might make possible an otherwise impossible shot, in some extreme situations.
If you shoot JPEGs right out of the camera (i.e. use in-camera conversion, all cameras initially capture in RAW)... then the 6D and 5DIII will be superior. You'll be able to use up to two stops higher than 5DII.
Also, the 6D and 5DIII focus systems are both rated to be able to focus about 2 EV lower light than the 5DII. I've found Canon's rating of the 5DII to be slightly conservative, it will still focus although slowly, about .5 EV lower than claimed (a wee bit lower light than 7D). But, 6D and 5DIII are both better.
6D has 11 point AF system. 5DIII has a superior 61 point AF system. 5DIII has 9 points visible, but 6 more "hidden" assist points, though those only work in AI Servo mode. 6D has one enhanced "dual axis" point, the rest are single axis. The 5DII has same for it's visible points, but two of the hidden assist points are also dual axis (so out of 15 total, that's 12 single axis and three dual axis... but, again, the hidden points are only usable in AI Servo, which isn't the 5DII's forté).
Both 6D and 5DIII use a newer processor, too, which helps support better AF performance... Nou doubt effecting speed, low light capability and accuracy.
Selecting an AF point on 5DII is done with a joystick that's fast to use. The 6D uses an 8-way button arrangement, but it's more easily reached with a grip on the camera, holding it in vertical/portrait orientation. The 5DIII has a joystick, too... and if fitted with a grip also enjoys a second joystick making reaching it during vertical/portrait shots particularly easy.
5DIII has a number of specialized AF modes above and beyond the basic modes of 6D and 5DII.
5DIII also has an active matrix focus screen, that reconfigures itself for different AF setups (and more). Some find this harder to use in low light. Both 6D and 5DII use simpler, unanimated focus screens. The are interchangeable, though, such as to add a grid to help with composition and alignment (the 5DIII has grid on demand built in).
I currently use 5DII, will likely upgrade to 5DIII at some point in the future, but am not in any rush because I also use a couple 7Ds for action shooting (and would almost certainly continue to use one or another crop cameras even with 5DIII). 6D is a viable alternative, but for a few reasons I might opt for 5DIII instead. One is that the 6D uses SD memory and I'd prefer both my cameras to be able to share the same handful of memory cards (7D, 5DII and one of the slots in 5DIII use CF memory). I also don't really need built-in GPS or wi-fi. The joystick (especially the dual joysticks with a grip fitted) and a few other factors will likely cause me to get the 5DIII.
But for now the 5DII still is a top notch and very up-to-date camera in most respects, that does all I need it to do, so I'm keeping my money in my pocket. To me "old" cameras are the vintage film cameras I collect (many of which are still perfectly usable, BTW). I don't even think of my EOS-3s as particularly old. I just don't have very much need to shoot film any more!
All three cameras can serve very well, depending upon individual needs.