Both sentences are correct and have the same meaning. "Ich habe hunger." is colloquial and frequently used, "Ich bin hungrig." is also correct, but nobody speaks like that...

Ich bin hunrig(adj). Ich habe Hunger(n) der Hunger. Ich bin durstig. Ich habe Durst. Ich bin frei. Ich habe Frei.

Both are correct and have the same meaning, ( more or less ) The difference between these two sentence is the grammar. Ich / bin / hungrig Subjekt / Verb / Adjektiv Ich / habe / Hunger Subjekt / Verb / direct object accusative (Akkusativobjekt). Do note that "Hunger" is a Subject, and therefore capitalized.