Nothing terribly original was said, but presumably the goal was to stimulate the imagination of the audience via the two fields of expertise represented here: evolutionary biology and astrophysics. Both Dawkins and Tyson emphasized the way science has enlarged our vision of the universe beyond our given natural biology of mid-range physical beings evolved to engage mid-range natural objects. Of course trying to extend our imagination through millions of years of biological evolution involves a stretch, but it seems that astrophysics' challenge to the imagination is much greater. Whether feigning incomprehension or serious, Dawkins admitted as much, asking Tyson to explain the notion of an expanding universe and what it means to be on the edge of it. Tyson rose to the challenge and attempted to explain it via analogy with a ship in the ocean. He claimed it need not so mysterious, but I believe he is incorrect.
Dawkins' explanation of evolution did not demand as much. Tyson acknowledged the counterintuitive nature of quantum mechanics, the dependence of physics on mathematics, and the fact that theoretical physics provides explanations that, in the ordinary intuitive sense, we do not understand. Science begins with sense experience, but instruments extend our range far beyond our innate sensory ability, detecting entities and phenomena we cannot directly perceive, and mathematics extends our ability to map reality beyond our limited and not completely reliable senses. Interestingly, once the counterintuitive nature of contemporary physics was acknowledged, Dawkins interjected the thought that mathematics becomes intuitive, so that physicists are able to navigate their terrain like pilots. He suggested an analogy with surgeons, who intuitively feel what they are doing with micromanipulating instruments, and in the future might conduct their surgeries mediated by virtual reality devices.
Tyson in turn introjected Dawkins' specialty into a consideration of exobiology, i.e. extraterrestrial life forms, and especially intelligent life forms. How do we know that we are intelligent in comparison to related animals whose difference from us might appear minuscule to a much more intelligent alien intelligence? Dawkins ran with this subject. Tyson reiterated his usual complaint against science fiction aliens being too anthropomorphic. Their discussion of the genetic code and what could conceivably be different indeed stimulated the imagination.
The questions subsequently posed by audience members were varied, but for now I will dwell only on one of them. Someone mentioned an impending abolition of the Philosophy Dept. at Howard University and asked for comments on the philosophy of science. Tyson responded that philosophy contributed to science until the 20th century, but with quantum mechanics became useless. While philosophy has other worthy objects of study, Tyson sees no further contributions by philosophy. Physics is high tech; armchair science is no longer possible.
Dawkins pointed out that philosophers could have easily thought of natural selection but did not. There are some good philosophers of biology, but these are the ones who are so thoroughly immersed in the science that they double as scientists.
I found Tyson's remarks especially revealing of how the scientific mind differs from the philosophical mind, and in this case I think he is dead wrong. He admits the largely counterintuitive nature of physics (while minimizing--at least this time around--the same viz. cosmology), and claims that philosophy of science is superfluous, when the revolutions in physics in the 20th century presented philosophers--and philosophically minded physicists--with the greatest challenges they ever faced. The nature of physical explanation and the theories that have emerged are far from uncontroversial, and the attempts to popularize them among the general public are fraught with pitfalls the scientists do not seem to understand. Tyson repeatedly warned against hubris, but how confident can one be now that physics is in for another revolution on account of dark matter and dark energy? (And I will add, what can Hawking possibly mean when he suggests that the universe was created out of nothing? Is this truly an empirical statement, and not philosophically controversial?)
Dawkins doesn't have this big of a problem as far as strictly biological evolution is concerned, but what about the metaphorical extension of biological evolution into social evolution? Is the concept of the "meme" a genuine scientific concept, or merely sloppy ideological reasoning by analogy? What about the sociobiology war of the 1970s?
All this and much more is fodder for a whole lot of additional discussion, as well as the question of applied science in the real world that is driven by big money, big business, and the military, which might not respect the integrity of pure research that characterize the scientific objectives of Tyson and Dawkins.