I've flown in both cabins extensively (travel SFO <> HKG quite frequently plus the 350 regional routes in Asia)

I don't disagree with what everyone is mentioning here -- plus, the fact that the 350 planes are simply newer is refreshing (no scratched surfaces compared to the 777).

That being said, you're on an 11+ hour flight. Chances are you're going to pass out and sleep for most of the flight, so sleep quality matters the most -- and in that respect there's little difference between the two flights.

Pick the flight that aligns to your schedule the best -- if you happen to be choosing between 873 and 893, I'd go with 893 (and get a nice sushi dinner in San Bruno -- ask me if you need recommendations!). Otherwise, getting to where you need to be on time matters far more than the marginal benefit of the 350 over the 777.