[Nyororin]

I have always connected 気持ちがいい with physical sensation, and 気分がいい with mood and emotion. Kind of leaning a tiny bit in the direction of 機嫌, maybe?

Something physically pleasant may obviously lead to 気分がいい, but I have also encountered it for unpleasant situations where the pleasure isn`t of the physical sort... And the actual physical experience itself isn`t at all.
気持ちがいい is also used where the pleasure isn`t necessarily of the physical type, but it always seems to imply that there is physical pleasure being derived from the situation.

A vague example... If you`re doing something and saying 気持ちがいい - it`s like saying that it feels good to do it. 気分がいい is like saying it`s a good feeling to do it.
Feeling good is not the same as having a good feeling... You can feel good about something that doesn`t actually feel good.

For 気持ちが悪い・気分が悪い, 気持ち tends to be something immediate. If something is visibly unpleasant, or if I actually feel ill it would be 気持ちが悪い. But if there was something emotionally disturbing, something unpleasant to even think about - it would be 気分が悪い.

Of course, this is just how I use and think of them.