Which one would be a better answer if you're asked "how are you feeling?" but you're not doing well and you do not want to discuss your troubles?
Either of these would be suitable in this case.
However, in some situations there may be a very subtle difference, brought on by the fact that people often say they're ok when they're not.
The subtleties are very hard to pick up - even for native speakers - and will usually differ depending on the relationship between the two people. If there's any doubt - and the relationship is strong enough - people may ask to clarify whether the answerer really is "ok" or "fine".
A common example of when this subtlety can occur is between a wife and her husband. When a wife says "I'm fine", it often means she really isn't - and an astute husband knows how to pick that up. "I'm ok", rather, is often more honest. Obviously, this example doesn't apply in situations where you don't know someone that well!