Honestly I am never a fan of SQ ultra long haul service and SQ 37 features the really bad meal arrangements with one supper after takeoff and then a full hot meal around 2/3 of the flight with a really bad so-called on demand snack menu. However SQ 11 features a rather annoying layover at Narita too. You get more food and better meals on the LA to Narita flight, but then there is only one single dinner service on the NRT-SIN segment.
I personally hate redeye flights, so I will pick SQ 11, but if you don't mind redeye and the strange SQ meal logical on these ultra-long-haul flights, go with nonstop!
Carfield