You should be able to use the == operator to make a comparison. Since you mention the Equals() method, you may have already read that and the above, but just in case:
Comparisons
The overloaded == operator can be used to compare two FStrings, or to compare an FString to an array of TCHAR*s. There is also the FString::Equals() method, which takes the FString to test against and the ESearchCase enum for whether or not the comparison should ignore case as arguments. If you want the comparison to ignore case, use ESearchCase::IgnoreCase, and if not, use ESearchCase::CaseSensitive.
TestHUDString.Equals(TEXT("Test"), ESearchCase::CaseSensitive);
Information on comparisons, conversions, etc for FString and related types, including the above, can be found here. Did neither of these methods work?