Vista - String handling: ordinal or invariant or current-culture?

Given this C#:-

String filePathname1 = ...
String filePathname2 = ...
if (String.Equals (filePathname1, filePathname2,
StringComparison.OrdinalIgnoreCase))

what would the equivalent PowerShell script be?

E.g. would it be:-
if ($filePathname1 -ieq $filePathname2)

I.e.
- do -eq and -ieq perform ordinal string comparisons?
- if not, then what?
- is the behaviour defined, and fixed for all time?
- if the behaviour is ordinal and I want a cultural comparison, do I have
to kick-up to .NET?
- how about the -lt and -gt operators?
- is the bevahiour documented anywhere?

Also, are there interesting and important things to note re. PowerShell's
value-to-string and string-to-value conversions (current culture vs.
specified culture vs. invariant culture)?

I think it would be great to have this sort of thing nailed down. It would
help me to be able to script in confidence.

Many thanks.

Andrew