Specifically, a planet similar in size and composition to our own, orbiting a star of the same class as our sun at about the same distance, and out on a spiral arm of the Andromeda Galaxy about as far as our solar system is from the galactic core. So all other things being equivalent, what would be different if we were in the Andromeda Galaxy? In terms of galactic environmental conditions like radiation from the core, mass, dust, etc.
Probably very earth-like, but the view would be different.
The Astrology page in the paper would be waaaay different.
I can’t see that there’d be any difference. M31’s core is rather larger than ours, and probably correspondingly more energetic, but radiation from the core of our Galaxy is far below the level of significance here on Earth, and it would still be far below significance on a planet in M31.
Difficult to say. Andromeda has more stars than the milky way, but may have less mass due to having less dark matter. I don’t know if Andromeda is more or less dusty than the milky way, that would affect the number of stars you’d see in the night sky, but probably not as much as the local stellar environment.
Our solar system is not in a major spiral arm. It orbits at roughly the same speed as the them, so passes through them rarely. This is probably a good environment for life to develop, as it help keep us away from other stars, which might supernova or perturb objects in the outer solar system into earth crossing orbits.
Maybe a brighter equivalent of a Milky Way in the skies, thanks to the larger size of the Galaxy?
It’s doubtful that such a planet would have a moon that is as large as the Earth’s.
How come?
I’m not so sure. I think it would be just as accurate if it was identical to ours.
I’ve heard that all life on Earth is DNA based, from the tiniest microscopic organism to the largest animals.
Life in other galaxies may not be.
Probably wouldn’t have these.
The specific biochemistry of the planet will probably be different (even if it is DNA-based, there are untold umpteen oodles of possible genetic codes to choose from), and Earth is probably uncommon in having such a large moon, so any given planet would probably differ in that regard as well, those are both just as true of any hypothetical planets around tau Ceti as they would be for a planet in the Andromeda Galaxy.
The significance of the galaxy from the point of view of a planet within it is pretty tiny, at least for galaxies like the Milky Way and Andromeda*. Even galaxies that are in the middle of spectacular collisions would generally not feel any different to planetary occupants. Calling it a galaxy emphasizes its character as a thing, but to the extent that a galaxy is a nearly empty collection of stars and other objects that are so tiny in relation to the distances between them, it is little more than a daydream in how it effects daily life.
Sci fi movies that show space flight through an asteroid belt make it look like a crazy billiards game of tumbling boulders, but it wouldn’t be. If you set up camp in our own asteroid belt, it would take years of careful astrometry and deep understanding and competence with celestial mechanics to figure out that you were in it. The only difference is in the gradual shift in position of starlike pinpricks of light from day to day, and they’d mostly be telescopic objects, not things you look up and see with your eyes.
Being in one galaxy or another would be ever so much more obscure an issue.
*Now, if we’re talking a more exotic galaxy with an unusually energetic core, like a quasar, life could be more like living inside an arc lamp…
Even a quasar wouldn’t be all that different-- If we’re assuming an Earthlike distance from the core, the planet will still get significantly more total energy from its own star than from the active core. Though the spectrum of the energy would be different, and that could cause problems. Probably not anything that life couldn’t adapt to, though.
So if the Milky Way were a quasar, but with Earth at the same distance from the core as we are right now – what would the night sky look like?
This is probably a gross oversimplification… but if the Milky Way has 2 billion stars and a quasar has an output of 1 trillion stars, it would look like the Milky Way but 50 times brighter. That’s not really all that bright.
The oversimplification assumes the same dust levels and same emission spectrum for a quasar as for our galaxy and its stars.
Shouldn’t that be 500 times brighter?
ETA: and isn’t there a bigger, first-order effect that in a quasar, all that light is a lot more concentrated, namely around the central black hole? So it’s not just a linear, overall increase in brightness.
You’d have to keep an eye out for Kelvans wanting to shrink you into a cuboctahedron… 
I’d be more worried about Paan’uri making the Sun go supernova.