Please specify what kind of comparison you expect :) Use StringComparison, or CultureInfo if necessary
Some applications need linguistic comparisons, others need ordinal type comparisons. A very general rule would be that user facing comparisons would need linguistic comparisons (use current culture), and security comparisons may need ordinal or ordinal ignore case. For some applilcations the default comparisons will not be appropriate. It is much better to understand the differences and use the correct version.
Additionally note that it is challenging to try to figure out what is going to be a match for the file system, URI/IRIs, etc. It is generally preferable to use the specific comparisons for the resource you're trying to compare. For example ?, & and other escaping rules in URLs, ..\, .\, :, etc in file names, etc. could all cause unexpected behavior if not properly tested for.