Burke's original Connections had an underscoring point, like most good films. It wasn't just a historic documentary, but how their perceptions of science and technological innovations stemming from those perceptions, effect us as a species and society.
The two Connection's series that follow on over a decade later are more or less light hearted looks at technological developments; inventions and developments. Burke narrates the observations of science and the technology that develops from new scientific discoveries, and impact in terms of the improvements of the lives of the people living at the time.
But missing is the societal commentary. Burke isn't serious here, but a bit more satisfied, as if to say "All the stuff I was worried about when I made Connections, has been resolved, and we are now living in a progressive time in which only better things will come." That's the tone I picked up from Connections 2 and Connections 3. Burke is no longer worried for the future, and the future is now evolving before us.
In short, his tone is more cheerful. The inventions and innovations are more positive, and don'e have the massive negative repercussions as some of mankind's inventions have in the past; i.e. from the cannonball to the atomic bomb to the ICBM.
Connections 2 and Connections 3 are more of a science and technology documentary, and simply that and nothing more. Still, they're interesting looks at science and inventions that Burke didn't touch on in his original series. They're an interesting watch, and from Burke could you expect anything less?