I sometimes see teens type:
Instead of typing:
What can you say about it?
As has been already stated, they are both contractions of "I have not," and neither is incorrect. In the USA, I would say that "I haven't" is far more commonly heard. The use of "I've not" sounds a bit more proper and old-fashioned.
Both are correct, just the difference in emphasis. If you want to emphasize the negative, don't contract not and vice versa.
They are equal. Neither is preferable. It is your choice, depending on which you like. A professional, like a speechwriter, might have a stronger preference based on more complex criteria, but for most people, there is no difference.
If you are feeling particularly bold, you might try
Which is a contraction of "I have not". That one isn't "accepted", but most native speakers will understand the meaning, and some accents pronounce "I have not" close to "I've'nt".