Armando is very refined and sophisticated, as opposed to Jon's more immature, uncouth mannerisms. Armando also appears to be a bit snooty.
Armando's shown to have an obviously strong dislike for Jon, although Jon is oblivious to it. Armando dislikes Jon largely for his stupidity as well as his klutziness and his immature, uncouth behavior, and the fact that he gives terrible tips.
Armando has never been shown speaking to Liz, but Liz is shown to be aware of the fact that Armando dislikes Jon. Also, given that Liz is much mature than Jon is and can be more sophisticated and refined than Jon is, Armando most likely would get along better with Liz.
- Once Armando revealed that the waiters drew straws to see who served Jon and Liz and he always lost because he was cursed.