There is no fundamental reason why a wider chain would be stronger, all else being equal. The 'easier to break a long stick' argument is apt. Plus, 3/32" has been developed more, and often includes more technological goodies like beveled plates and bushingless designs (which are usually regarded as just as strong, and smoother than bushings).

MTBers have been putting ludicrous amounts of torque on their chains with no problem, and you won't have that problem either.

The only reason I'd go 1/8" chain is for retro goodness, or if that was the only cogs and rings I had around. Nothing wrong with retro goodness, just in this case realize that it isn't a decision based on durability.

The one durability concern I hear about a lot (and not just in the fixie world) is breaking master-links. Masterlinks are great if you aren't putting much torque on your chain, or for making a quick fix on the road, but if you are riding brakeless, I'd invest in a good chaintool and install your chain the right way. If you ask around about chain breakage horror stories, 9 times out of 10 it was a master link that failed.

peace,
sam