1/8 chain on 3/32 rings/sprockets can be a bit noisier but I imagine it's minimal. I don't see how, like-for-like, 1/8 can be any stronger than 3/32. The extra width won't add strength. It's more likely that a lot of 1/8 chains are built for track riding and are made stronger but you'll get strong 3/32 chains too. The strength comes from how they're made. Izumi track chains, for example, use good quality, bushed pins and are joined with a but and bolt - but then they're 25 quid a pop.
The main advantage of running 1/8 is that you know any combo will work