"Neanderthals may not have been able to coordinate such a large social group as modern humans".
It is quite possible that modern humans are not able to coordinate as large social groups as they now have to. No system of government or economic management has yet been proven over a long enough period to engender confidence. For example, no system of paper money has ever lasted more than a century or so without undergoing catastrophic inflation. We are just about getting to the critical point - and it shows.
Neither have we been able to find a system of government that can handle billions of people fairly, safely, and sustainably. A visiting Martian would perhaps be puzzled by the complete absence of any attempt to research, let alone safeguard, the future security of the human race. Instead, everywhere we see businesspeople frantically enriching themselves while politicians plot their strategies to gain or retain power. Very few, if any, think more than five years ahead.
According to an old story, during Nixon's visit to China in 1972 someone asked Zhou Enlai what he thought were the consequences of the French Revolution. "Too early to say," he is supposed to have replied, thus giving a fine example of long-term thinking. It's now thought he was referring to the disturbances going on in France at the time, not in 1789, but it's still a nice story. Just so, it's far too early to tell whether modern man has really done much better than the Neanderthals. Indeed, we may turn out to have done much worse, if we pull much of our ecosystem down with us.