If you ran into a common joe on the Street and asked him if he thought people today were better than people were 400 years ago, naturally he'd say yes. That's just how people are. It makes sense for the TNG people to think they were better than their predecessors. Annoying yes, but realistic.
Actually, if anything, the tendency is more often the reverse. For thousands of years, as evidenced by ancient mythologies, people have believed that the past was a golden age from which humanity has degenerated. Every aging generation looks on "these kids today" and complains about how they've lost sight of society's values, or how their music and entertainment are mindless, talentless drivel compared to the superior stuff of the past. And countless people believe that the world is getting more dangerous, more violent, more morally degenerate, and are nostalgic for the more peaceful, simpler times of the past.
Of course, the truth is actually pretty much the opposite. Today people are healthier and safer from disease (at least in the developed world), there's more freedom and opportunity and better standards of living, and the average person's odds of being a victim of violence are much lower today than they were in the past. Humanity actually is getting better on the whole, albeit with some backsliding here and there.