It's really a User Preference thing. TNT Tracks a small amount of info compared to HS, that small amount is all that CIT needs to display everything you see on the Site now. HS is more of a just-for-the-User Program, it tracks and sends CIT all the info TNT does, and then some.
Everything else that HS Tracks that is not sent to us is just details about your Characters slotting (Power Recharge times, Accuracy, Debuff Percentages, etc) that you the User could review and make note of in the event that Character could use some improvements. None of that is used at CIT at all.
So all in all, you only need to run one, but which one to run is up to you.