As user68186 commented there is a fix for the black screen issue.
Moreover, there is always a possibility that Ubutnu 12.04.3 will also have the black screen issue or some other issue.
Thus in deciding whether to use 12.04.03 you might also want to consider the fact that it is an LTS (Long term support) release and thus is guaranteed to be supported for 5 years after it's release, which is in April of 2017.
13.10 comes with the latest and greatest software, but it's support will end 9 months from it's release date which is July 2014. Because of this you may want to choose a different Ubuntu derivative that uses a rolling release.
So if having the most up to date software is most important to you, you likely should choose 13.10, where as if you would prefer not to need to update your operating system in 2 years, than 12.04.3 is likely a better choice.
See this question for more on why Ubuntu limits support.