True, there would be that difference, but the constellations would be the same as here on Earth.

Did you ever see the movie 2010? At the end, after Jupiter becomes a small star, Roy Scheider’s character talks about a new generation growing up that will never know a dark night sky. This is not true. Planets orbiting Binary’s would have dark night skies some of the time (as you pointed out). In the Alpha Centauri System, Proxima would not be bright enough to chase away the night around any planets orbiting A or B.

Here is an interesting article that was taken out of the Astronomy Magazine (That is where I first read it several years ago.

Terrestrial planets would have stable orbits out to about 2 Aus from Alpha Centauri A and Alpha Centauri B. If you could drop our terrestrial planets around each star, Earth and Mars would be in A’s life zone, while Venus and Earth would be in Life Zone.

I wouldn’t rule out worlds around Proxima about having life. True it is a dim, flare star, but life has a way of surprising us. I mean, 40 years ago who would have ever though that Europa, a Moon-sized moon of Jupiter, would an oceans of water.

The Alpha Centauri System will have to be studied closer once we develop scopes capable of seeing terrestrial sized planets around nearby stars.