FXCop typically prefers `OrdinalIgnoreCase`. But your requirements may vary.
For English there is very little difference. It is when you wander into languages that have different written language constructs that this becomes an issue. I am not experienced enough to give you more than that.
OrdinalIgnoreCase
> The StringComparer returned by the
> OrdinalIgnoreCase property treats
> the characters in the strings to
> compare as if they were converted
> to uppercase using the conventions
> of the invariant culture, and then
> performs a simple byte comparison
> that is independent of language.
> This is most appropriate when
> comparing strings that are generated
> programmatically or when comparing
> case-insensitive resources such as
> paths and filenames.
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InvariantCultureIgnoreCase
> The StringComparer returned by the
> InvariantCultureIgnoreCase property
> compares strings in a linguistically
> relevant manner that ignores case, but
> it is not suitable for display in any
> particular culture. Its major
> application is to order strings in a
> way that will be identical across
> cultures.
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>
> The invariant culture is the
> CultureInfo object returned by the
> InvariantCulture property.
>
> The InvariantCultureIgnoreCase
> property actually returns an instance
> of an anonymous class derived from the
> StringComparer class.