"Long time, no see" is a casual way of greeting somebody who (as you might guess) you haven't seen for a while. So, if you meet a friend after some time apart you might just simply say to them "Long time, no see!" and then launch into a proper conversation or, perhaps, you might say "Hey Marzi, long time, no see - how are you?/How's things?/How's it going?"
It's been *QUITE a while (not quiet - which means without much or any noise) on the other hand is more a general observation about the length of time and might be used anywhere in a conversation where an assessment of how much time has passed is appropriate.
So you might open a conversation with "Hey Marzi, it's been quite a while, how's things?" but equally you might use it to respond to a question:
"How long has it been since you were in college?"
"It's been quite a while!"
"How long has Marzi been gone?"
"It's been quite a while, perhaps we should look for her..."
I hope that helps.