I think drive train durability would be the main advantage of 1/8 over 3/32. 3/32 is always going to be a bit lighter, but this is rarely a concern on the track. Some sources I've read describe endurance track racers using 3/32 because the chains are less rigid and easier to push over longer periods of time. 3/32 was probably more commonly used for track and fixed gear when the equipment was more interchangeable. Modern 9+ speed chains are said to be too narrow to be usable on 3/32 fixed cogs.

Here's a couple links that discuss the subject a bit:

http://www.kenhart.com/track/FAQ_Roa...ack_Chains.pdf

http://www.ridethetrack.com/pdf/trackracing_intro.pdf