It would be better than living your entire life in a literal cage on earth. But I think it would be worse than even being a slave on earth. A slave can touch grass and hope to run away. A person born on a generational ship would be effectively enslaved (to perform necessary ship duties). You mention 'cutting edge healthcare', but on earth that requires the substantial and diverse resources of an industrial civilization. The research of millions of people and the infrastructure to breed nuclides and manufacture precise machinery. Does this generational ship have a modern chip fab on it!?