I'm no expert, but i'll try....

1/8" advantages:
--more quality chainrings available in 144bcd (which i've)
There are plenty of 144 BCD 3/32" chainrings available.: TA, Sugino 75, DA, Blackspire, Salsa, Vuelta. I've even got brand new 48 and 50 T Sugino Aero Mighty Rings lying around if you want.

--works on 3/32 stuff too
true, 1/8" chain works with 3/32" cogs. Kogswell, among others does this. It tends to be a bit moisier though.

--stronger/more durable
--seems like there are more cogs around on, say, ebay and the Int'l cog exchange, so easier to get slightly-used (thus cheaper) cogs in this size.
durability debatable, stiffer? probably. new 3/32" cogs and rings tend to cost less than their 1/8" counterparts.

1/8" disadvantages:
--chain weighs more
true

--would have to buy another $40 park chain tool (god i love those things)
you could always make one out of some scrap 1/8" chain

--couldn't swap cogs with my 3/32" partner (at least, she couldn't use mine)
--harder to find replacement parts when on our cross country fixie tour (not for a while yet)
you could both run 1/8" chain

--more fussy about chainline being perfect
makes sense, 1/8" chain is less flexible