To be honest the best place to look for duplicates is in the belly of the beast - the database. Much easier/faster.
However, if you must do it in the code, you could try StringComparer.OrdinalIgnoreCase:
StringComparer comparer = StringComparer.OrdinalIgnoreCase;
var caseInsensitiveResults = ctx.SomeObjectSet.Where(x => comparer.Equals(x.Field1, x.Field2));
As the .Equals method of the StringComparer object returns true/false, you can use it as the predicate.
Are you trying to look for duplicates in one table? Define "duplicate" in your specific scenario, might help us help you.
EDIT
Since your saying your looking for duplicate rows in a single table, the above won't work. It was just an example.
You'll need to use that comparer code in the GroupBy clause instead.
However, i still think you should do this in the database.