В этом случае правильный вариант "to feel resentful". После следующих глаголов "sound, feel, taste, smell" должно употребляться прилагательное.

That really depends on what you want to say. 1. He feels resentful towards something or somebody. 2. He feels a lot of resentment in his life. "Resentfulness" is a very abstract noun, and is usually preferred by Russians and Germans.