My experience has been pretty good. I get iMessage notifications on my Mac desktop, Mac Air, and on my iPhone. If I read a message on one of my Macs, the notification is cleared on my iPhone. Same experience if I read it on my iPhone first; it clears the notification on my Macs.
The only issue I have seen is if the notifications come to my device after I have read it on the other device. For instance, if my MBA is "sleeping" and I receive iMessages and read them on my iPhone. In this case, I receive the queued up iMessage on my MBA when I "wake" it up.