[jamest (OP)]

Pamela wants to know: 'On Earth, roughly 99% of the element carbon is Carbon 12 and 1% is Carbon 13. Would chemical elements exhibit the same isotopic distribution on other planets? What difference would this make?'

[Bored chemist]

Within the solar system, largely, yes.
But, for example, the moon has "more than its fair share" of helium 3.

Other stars have different distributions of elements and it's reasonable to image the isotope ratios would also be different.

It seems that people are working on finding out.
https://www.aanda.org/articles/aa/full_html/2016/11/aa29273-16/aa29273-16.html

[alancalverd]

From Wikipedia:

The primary natural source of carbon-14 on Earth is cosmic ray action on nitrogen in the atmosphere, and it is therefore a cosmogenic nuclide.

So you would expect that the distribution of cosmogenic nuclides and their parents will depend on the radiation environment of the planet, even if all the planets were formed at the same time and by the same mechanism, and there was no gravitational segregation of atmospheric gases.

So the answer is "not quite."

[Bored chemist]

From Wikipedia:

The primary natural source of carbon-14 on Earth is cosmic ray action on nitrogen in the atmosphere, and it is therefore a cosmogenic nuclide.

So you would expect that the distribution of cosmogenic nuclides and their parents will depend on the radiation environment of the planet, even if all the planets were formed at the same time and by the same mechanism, and there was no gravitational segregation of atmospheric gases.

So the answer is "not quite."

The cosmic ray background is from outside the solar system. I don't know how "universal" it is, but I think the answer is "fairly".
And the C14 to C12 ratio here on earth is about 1 to 1000000000000
So, unless if you had a planet which started with lots of (atmospheric) nitrogen and no carbon, I don't think you are going to change the isotope ratio much in absolute terms.
Changing the magnetic field might make it more interesting.

[evan_au]

Radioactive C14 present at the formation of the Earth would all be gone (half-life 5,700 years), but it is continually produced by cosmic rays smashing into Nitrogen in the atmosphere.
- If a planet had little Nitrogen in the atmosphere (like Mars), then there would be less C14.

Stable C13 and C12 isotopes are produced in supernova explosions, but the ratio of them would depend on the type of star exploding.
- Red giants shed a lot of their atmosphere, and the carbon present here would be primarily C12, formed by fusing helium.
- So the isotopic composition of carbon in a planet or star would be determined by the mix of events seeding the molecular clouds from which they formed.

Even on Earth, the ratio of C12 and C13 varies slightly in different places, due to plant photosynthesis (plants prefer C12 to C13).

More dramatically:

at the time of the Permian extinction 252 Mya when the [C12/C13] ratio changed abruptly by 1%

Presumably, a large source with a different C12/C13 ratio was dumped into the atmosphere.
For more detail on this event:
https://en.wikipedia.org/wiki/Permian%E2%80%93Triassic_extinction_event#Dating

With elements having very different origins, the concentration would vary dramatically with the events forming their molecular gas clouds.
- The heavier elements (Silver and above) are mostly formed in neutron star collisions/disruptions.
- A difference in the proximity of these events would make a big difference in the concentration of heavy elements in a star or planet
See periodic table at: https://en.wikipedia.org/wiki/Nucleosynthesis#Timeline