For me, the phrasing "better to be right" strongly means public acknowledgment, getting someone else to note one's rightness. So it's the least important. In fact, the more fundamental meaning didn't even occur to me until I saw the debate in comments. I guess I could call that "getting it right", "being accurate"? Anyway, with THAT meaning, I think it ranks above happy but below good. If good was kind/nice, though, I'm not so sure.