It's a tough question you raise, Stephen. Since you're using capital letters, you are implying that these are values placed above the individual. Maybe it's not so cut and dry as one having more value than the other. Perhaps they each have their place in different scenarios.
Great questions you raised, jack! I would venture to say that if you're dishonest with someone but they never find out, that would still fall under being disloyal. Part of loyalty is honesty in my opinion.
However, the interesting debate that you raise is someone not knowing of your dishonesty, and does that make being loyal more important than honesty because it encompasses both things? If someone doesn't find out, has the dishonesty caused any harm?
Thoughts, anyone?