I have a L1 visa for my work in the USA. I also have a second British passport for my visas to other countries (China). I have approved visas. What passport do I show when I am leaving USA ? The one with the China visa in it or the one with my work visa?
This works exactly the same as with dual nationality, see the canonical answer: I have two passports/nationalities. How do I use them when I travel?. Treat it as case 1.
In this case you entered the USA with your USA visa passport, so you have to use that again when leaving the country (checking in). In China you show your passport with Chinese visa.
Keep in mind that the USA does not have exit checks. The airline will register you instead. So always use the passport you entered on to leave. The airline will also want to see you are allowed into your destination country. Showing your other passport along with a quick explanation will do.