'Feel' can be followed by either an adjective or a noun. I felt guilty or I felt guilt I felt hungry or I felt hunger There's no change in meaning, i.e. the information expressed is the same. However, the noun sounds quite formal whereas the adjective is much more everyday.

The others have covered it pretty well. Both versions mean the same thing. The slight difference: I feel guilty. = GUILTY is my state of being. I feel guilt. - GUILT is the emotion I'm feeling. In my opinion, the first sounds more personal, as if one identifies with the guilt, while the second is slightly more objective. But it's a slight difference.

Of the two, "guilty" is the harder one to explain. "I feel guilt" is straightforward. It is just the same as "I feel happiness" or "I feel loneliness". "Guilt", "happiness", and "loneliness" are names of moods that you can feel. "I feel guilty" is a more interesting grammatical construction. Normally, the construction SUBJECT + VERB + ADJECTIVE does not work. For example, all of these make no sense: "I jump slow" "I sing beautiful" "I eat tasty" Not only don't they make sense, but they are grammatical impossibilities. In each case, an ADVERB would be required to make sense: "I jump slowly" "I sing beautifully" "I eat voraciously" Why is "feel" different? It is one of a few very select verbs that are allowed to take an adjective to refer back to the subject. Other verbs that have this special property are: "to be", "appear", "look", and "seem": "Jack is happy" "Bill appears sad" "The children look tired" "The test seems difficult" To learn more about this phenomenon, study "Predicative Complements".

‘I feel guilty’ is a common expression which might often be used to express a feeling that isn’t intense and may be exaggerated. I feel guilty that I didn’t help clean the kitchen after dinner. I was just too tired this evening. Do I ever feel guilty - she gave me an iPhone and I gave her a scarf. (Informal social rules have been broken.) ‘Feeling guilt’ is rarer and more serious. He felt guilt for abandoning his children. (The duty to care for your children is important)