Will an 1/8' chain and cogs wear slower than 3/32' chain and cogs for single speed / fixed gear setup? Will an 1/8" chain and cogs wear slower than 3/32" chain and cogs for single speed / fixed gear setup? What about using an 1/8' chain mismatched on 3/32" chainring and cogs?
I don't remember where, but I read once that because a 3/32" chain is more flexible laterally than a 1/8" chain, it is more tolerant of imperfect chainlines.  This makes sense to me, but I haven't seen any numbers to support it.  So with an imperfect chainline you might see faster wear with 1/8".

I suspect the difference in wear is imperceptible, especially with a steel cog.  The combination of a 1/8" chain, imperfect chainline, and an aluminum 3/32" cog would probably be where you'd see the most increase in wear because you add a slight bit of play where the chain interfaces with the cog, but I still doubt you'd notice much additional wear.