＊Note that there expressions convey different meanings and need to be used carefully.
気持ちがいい is used when the speaker feels good upon being exposed to an exterior stimulus. 気分がいい is used when the speaker expresses a great feeling coming from inside himself such as psychological exhilaration or a physiological sense of well-being.
Sentence 1 means that one “feels great in breathing fresh air or being out on a sunny day after a long spell of rainy or cloudy weather.”
Sentence 2 means that the speaker feels his physical condition is good.