Advantage to the 3/32": they're usually quieter if everything is set up right. And supposedly they're stronger, although many will argue. Good track components come in 1/8" commonly, which might be prohibitive. The best chains (arguably) are all in 1/8" like the Izumi's, and if you want a nice colored one by KMC, they only make them in 1/8".
EDIT: This is nicely contradictory to the above post. Just what I've found.