They are both correct. Here are some more examples which involve feelings:
1. I have never felt so angry. = I have never been so angry.
2. I have never felt so sad. = I have never been so sad.
3. I have never felt so depressed. = I have never been so depressed.
4. I have never felt so exhausted. = I have never been so exhausted.
These I would write with just "been":
1. I have never been so late.
2. I have never been so on time for a meeting.
Although....
Summer has never felt so late. = It seems like summer has never arrived this late before.