Laura's explanation is good.
Curiously, I have never said or heard of either of them, unless in a conversation with a non-native speaker of Mandarin. I think it may have something to do with Chinese mentality, we are relatively reserved, introverted.
I wonder if these two are "made-up" expressions in Mandarin textbooks, to serve as equivalents to something in English, like
Nice to see you. Nice to meet you.
or to something in French, like
Enchanté de vous voir. Enchanté de faire votre connaissance.