I don't have any objective testing results, but an argument could be made for either being stronger: Eg., the shorter pin length on the 3/32" chain induces less stress on the side plate, therefore rendering it a stronger chain. On the flip side, a 1/8" chain with its heavier-bigger plates and pins just by sheer materials alone, render it a stronger chain. But now let's throw a monkey wrench into the equation and go with the mass to diameter ratio and which one ends up the strongest???? I have no idea. I have never snapped a chain either 1/8 or 3/32 that was due to chain failure and not my own error.
That all being said, I don't think the focus should be so much on the chain, neither size: 3/32 vs 1/8, nor type: bushing vs bushing-less; as opposed to the other components of the drivetrain. As has been said, the best/roundest/most precise rings are almost exclusively 1/8". If you want to run your chain tension high, you better be as close to perfectly round as possible, and at least it seems to me that 1/8" is the way to go there. When considering rings, as opposed to chains, size does matter. Given similar engineering and materials, a 1/8" ring will be stronger and hold its shape against deformation under load better than a 3/32" ring, I don't think there could be any argument there.
zac
I agree with mihlbach that *any* reasonable bike chain has more than enough strength. But we need to know what strength means - basically, is says if a chain is hung from a fixed point, what weight will cause the chain to break or fall apart. To use an old saying, the weakest part is the weak link... Or in this case, the weakest part of the link. My guess is that the failure mode is deformation of the side plate where it is bevelled in to trap the roller. I think that bevel bends allowing the roller to come free. If I am right, then mihlbach's comment that chain width is irrelevent is true. Since the side plates are likely much the same thickness and material, both will fail at the same weight.
As for the comments about frictional losses, it might be 1/2 of 1 % of the total energy. In other words, who cares!