I've wheeled in 6+ feet of snow and on snowy roads and would say the larger chains have no advantage vs my cable chains. No science, just comparing mobility of the same group of chained vehicles vs my cable chains.
I have a theory on why. First, understand that chains basically present what amounts to a short paddle to a snowy surface - a third of an inch tall and as wide as the tread - for a tire profile that would simply not be suitable for everyday use on the road. Ditto cables (mine have short lengths of thick walled pipe on the cables that contact the ground). The difference is the cables seem more stable because the cables conform and fit better - for less movement on the treads.
If the tire's in a foot of snow, let's say there are 4 cables or chains in contact with the snow. Apply torque. Let's say one of the chains slips until it goes taut rather than stays put against the tire. What you have then is only 3 chains providing a grip at the crucial onset of movement, and a far higher chance the tire will spin. Interestingly, the 4th chain won't go taut until the other 3 slip. By contrast, the cables across the tread are all in equal tension and won't move (or will move the exact same distance) when torque is applied, so the force on them is more equal. They seem to provide more traction since one or the other will not break loose first.
Having said that, I think a properly set up set of regular chains could duplicate this stable condition, but they're much more difficult to get in this state. And they seem to move after a while even when originally set up correctly. These were experienced chain users and every half mile or so (about an hour) of trail wheeling one or the other had to stop and mess with a chain. I never had to.
For transitional use (install them to get home, or up someone's steep driveway), the cable chains I have are a breeze to put on. They have an integrated hoop for quick, faultless positioning, which also is why they're so stable in use.
I suspect for solid thick ice the "bar chain" (sharp little bars welded to the links) traditional style would be the very best as they tend to slap the ground and dig little holes. But for all around use and transitional use I feel a quality set of cable chains are hard to beat.
Whatever you get, don't scrimp on the chain tensioners. Get the good ones, and have at least 2 spares on hand as the greater the chain tension the closer you'll get to cable performance. Plus, eventually you'll see one of those chain tensioners go whizzing by the windows.
DougM