What size is more suitable for fixed gear bikes?Most single gear bikes,bicycles with internal gearing and track bikes use the wider 1/8″ when 3/32″ is the common chain size for the multi-speed bikes.You can easily find both types of chains and you can buy fixed gear sprockets for both sizes.
You can use chainrings that are design for 3/32″ chain with 1/8′ chain(of course i cannot see the reason to do that) , but not the opposite.But it is not something that i would try with the sprockets(use 3/32″ chain with 1/8″ sprockets).
I have created and ride fixies with both chain size.If you convert a multi-speed bike to a fixie i would generally advise to continue using the 3/32″ (derailer) size. It is lighter,no less durable or reliable than 1/8″, more compatible with your existing chainwheels, and most likely is going to run smoother if the chainline is less than perfect.
If you have perfect chainline and you do not care the cost of changing chainwheels and chain then go with the 1/8″ chain.