EK has risen rapidly in the airline industry to become one of the manufacturers' most important customers. However, Singapore Airlines is a longstanding customer for both Boeing and Airbus, while Emirates has a much shorter history with them.
Socially, I think that Emirates is perceived as being "nouveau riche" compared to Singapore's "old money". I also think that SQ
is perceived as being a real "gold-chip" customer that is expected to be with us for many years. On the other hand, EK
's future, though bright at the moment, could easily become tenuous if the winds of political and fundamentalist change blow cold in her region of the world and upon her "wings".
In summary, Singapore Airlines is, by far, the more prestigious of the two carriers.