The short version
Two opposite approaches to nasal breathing. Hostage Tape forces it via mouth seal. Intake makes it easier via nostril dilation. Different mechanisms; can be stacked.
When is Hostage Tape the right pick?
If you're committed to forcing nasal breathing via mouth seal and you've ruled out sleep apnea — Hostage Tape is the right shape. Direct mechanism, subscription convenience.
When is Intake Breathing the right pick?
If you can't adapt to mouth tape — Intake is the right shape. Comfortable from night one, makes nasal breathing easier without forcing it. Dilators can also quieten snoring and hide possible sleep apnea — if apnea is possible, see a doctor first.