The plus of 1/8" chains is that they are harder to throw off the cog. Not an issue on the track where cranksets are of high quality and round and chain slack is carefully monitored. Where flats are never repaired then the wheel but back on in the dark by an inebriated rider. Where potholes are never hit. But in the real world of road fix gears, 1/8" chains are simply more rock-solid and stay on better, allow you to use cogs and chainrings longer and are more forgiving with lower quality cranksets, hubs and cogs (that don't run especially round, leading to the chain tightening and loosening every revolution and requiring more slack at its slackest to keep the tightest from being too tight.
I started on 3/32" chains and rode them for 25 years. Life has simply been better since I switched. 1/8" starts at higher prices, but over time, that levels out as everything lasts longer.
Ben