It seems to me that 好久不見 exists as an idiom, which might make it sound more casual (“long time no see!”), whereas 好久沒見 doesn’t seem to exist as an idiom, which might make it sound more matter-ot-fact and appropriate for formal use (“I haven’t seen you in a while.”).
I recently greeted a Chinese taijiquan teacher, whom I hadn’t seen in a while, with 好久不見, but afterwards thought that maybe 好久沒見 would have been more formal and appropriate.
My old textbook only mentions 好久沒見 and not 好久不見, though I had already learned 好久不見 from some other phrasebook. A Google search on either phrase turns up many hits, so both do seem to exist. Asking our AI overlords, I received an answer that 好久沒見 may carry the nuance of a previously planned meeting that didn’t happen.
I also found some discussion board where apparently someone from China said (using simplified characters):
Anyway, I’ll stick to 好久不見. And I’m glad that I didn’t accidentally use 好久沒見 with my teacher, to avoid giving the wrong impression of “really missing him or her”!
My suspicion is as a foreigner if you said the 沒見 version, people would just assume you got it wrong. I understand that it is apparently a correct way to say it, but there are different rules for dummy waiguorens.