I wish to calculate correlation between external rating of accounts and internal ratings of the accounts in my branch. Which out of Pearson correlation or rank correlation will be better to use and why.
You should test the normality of your data. If both your internal and external ratings fit normality the best is to use Pearson correlation, which is parametric test.
If they don't fit normal distribution you have to use Spearman rank correlation, which is non-parametric.
It is a rule that's applicable to almost all test that the parametric version gives the more reliable results as long as the assumptions are not violated.