"Long time no see" is very informal. It dates from racist American "western" movies of the 50s and 60s which showed indigenous people ("Indians") as primitive, warlike people who spoke little English. A greeting between native people and white people who knew each other was almost always "Long time no see." The phrase has not completely disappeared. However, I personally have not heard in it in the last 20 years. "It's been a long time (since we've seen each other)" and "It's been quite a while (since we've seen each other)" are neutral, natural statements.

"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.