I was a devoted watcher of and listener to the Sagan version, and so far I have enjoyed greatly the Tyson program and, I hope, I've learned from it.
Still, I'll complain this far (excluding using a buggy whip with a buggy with horses to illustrate movement faster than the speed of sound, which I'll trust PETA to cover).
Tyson presents Giordano Bruno (1548-1600) as a great martyr to science for his standing up for his belief in an infinite universe and standing up to the Inquisition and getting burned for it. Two things: first, Bruno was burned more for his heresy of pantheism — which got Baruch Spinoza in trouble later — than for his cosmology, and, second, he was, personally, something of an asshole: an unpleasant person who could have stayed out of Italy and (probably) out of the flames. The Inquisition was despicable because it tortured and killed people for all sorts of reasons, not just because one of them was the usefully radical thinker Giordano Bruno. (Galileo was a different story: he was naïve enough to go to Rome to speak Truth to Power, but sensible enough to shut up when Power showed him the horrible things they'd do to him if he didn't shut up.)
Also I am definitely prejudiced against Isaac Newton after listening to Neal Stephenson's BAROQUE CYCLE novels, but even allowing for that I'll throw in that Tyson is soft on Newton and, so far in the series, unfair to Newton's opponent on the invention of "the Calculus," Gottfried Leibniz. Stephenson's fictional villain aside, Tyson understates just how weird some of Newton's ideas were. Newton's dedication to alchemy was a bit much moving into the 18th century, and the guy was an oddball among exegetes of the Biblical Book of Revelation, and there's an impressively high bar for weirdness among people obsessed with Revelation.
Far more important, Tyson usefully takes on Creationists, but, like most people arguing for scientific cosmology and world-view, Cosmos argues past the God-folks' major concern — and, therefore, argues a bit in bad faith.
Tyson and Cosmos beautifully demonstrate how scientific thought has, so to speak, moved human beings from the center of the universe. To start with we have moved from the center, in terms of the physical structure of the cosmos as we usually think of it. After that, we have been decentered in terms of time. What scientific cosmography, cosmology, and — to warp a word's meaning a bit — scientific "history-ography" has done is show us that the traditional idea of human centrality is a natural enough illusion, but an illusion.
And here I'll quote one version of several of my quotations of Robert Ardrey on what Tyson et al. don't get into with the human implications of that illusion.
In African Genesis (1961), Robert Ardrey recounts a theory from the early 1940s: The Illusion of Central Position. According to the theory, this illusion "is the birthright of every human baby." A baby boy enters the world and "Bright objects appear for his amusement, bottles and breasts for his comfort. His groping consciousness finds no reason at all to doubt the world's consecration to his needs and purposes. His Illusion of Central Position is perfect" (African Genesis 144; ch. 6). With maturity, however, the illusion is undercut and the child and then the man comes to a truer perception of his place in the scheme of things.
Nonetheless the theory grants that should a man ever attain a state of total maturity — ever come to see himself, in other words, in perfect mathematical relationship to the tide of tumultuous life which has risen upon the earth and in which we represent but a single swell; and furthermore come to see our earth as but one opportunity for life among uncounted millions in our galaxy alone, and our galaxy as but one statistical improbability, nothing more, in the silent mathematics of all things—should a man, in sum, ever achieve the final, total, truthful Disillusionment of Central Position, then in all likelihood he would no longer keep going but would simply lie down, wherever he happened to be, and with a long-drawn sigh return to the oblivion from which he came. (145; ch. 6)
Now when I'm operating in scientific or scholarly mode, I am a good materialist (though recognizing that nowadays even the concept of "matter" is problematic), and I accept a universe of, in Carl Sagan's words, "billions upon billions of stars" and galaxies; and I would like every human being on Earth to accept that universe. But that mode of scientific thought is responsibly realistic only when the "hard" sciences are combined with the "softer" ones dealing with human beings as such, and with philosophy.
Human beings need myths of human significance, or Buddhist techniques of embracing nothingness, or instruction in a bracing philosophy like atheistic Existentialism that starts with human insignificance, moves into despair such as Ardrey describes, and then tries to carry on. What we don't need, what is acting in bad faith, is expanding the universe infinitely beyond human scale and then failing to deal with the human implications of such ultimately philosophical moves.
There are theistic Existentialisms and other philosophies where one takes a leap into the absurd and says God exists and functions and for some mysterious reason cares about the physical universe and maybe consciousness down to the minute and trivial level of human beings. Such beliefs are respectable, I think, so long as one robustly admits the leap of faith there, and insists on its absurdity. What annoys me is ignoring the problem or — what Tyson is not guilty of but some are — what annoys me is people holding in contempt a leap into absurd faith in God while asserting the downright lie that we humans, in terms of The Big Picture, are somehow important or that human life has value beyond that which we have chosen, egotistically and arbitrarily — and necessarily — to assign it.
Carl Sagan is one of my heroes, and I strongly respect Neil deGrasse Tyson, Seth Macfarland, and the other people responsible for the new Cosmos. But I hope someone on local access or in a very small niche market gets out a money-losing, unpopular show on Cosmos and Chaos and the Human Implications of a Rigorous Materialism.
Nowadays to assert the literal truth of creation myths such as the two in the Biblical Book of Genesis is to lie and to lie ignorantly and arrogantly. To accept the Cosmos concept of the universe as, to put it gently, unproblematic for human worth and dignity, is also to lie.
I'm a life member of the American Civil Liberties Union and condemn the Roman Catholic Church for their condemnation of Giordano Bruno and prosecution of Galileo Galilei; to punish people for beliefs and speech is to do evil. This much, though: in Bruno even more than Galileo, the Church sensed danger, and, that far, in the long term — for secular Humanists as well as for religious folk — they sensed correctly.
ADDENDUM, 1 Jan. 2018: Tyson does get into human smallness, but in a cheerful, upbeat way <http://www.wbur.org/onpoint/2018/01/01/neil-degrasse-tyson-brings-astrophysics-down-to-earth>.