Which chain is less likely to come off 1/8 or 9/32?
 

Since I have very good front and rear brakes on my bike, I'm not worried about it breaking.

All else being equal, which chain is less likely derail?

since the 9/32 doesn't exist, i think it'd be pretty hard to throw it. that said, it would be harder to install.

I think you meant 3/32. Anyway, as long as your chainline is straight it shouldn't make a difference.

The chain that fits the width of your cogs is less likely to derail..

Having your chain tensioned correctly and cranking down on your axle nuts is going to have a much larger effect on chain throwing than chain width.

What they said.
Either size will work fine, and as long as the components of your drivetrain are consistently the same size, and adjusted correctly, you shouldn't have any problems.
With that out of the way, I'll say that I personally use a 1/8" chain on my fixed gear, since I go fast and am not a tiny guy. Guess I have a mental block about it, but I tend to operate under the impression that a 1/8" bmx chain will be stronger and less likely to break.