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 Hostage Tape is 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 Intake Breathing is the right pick
If you can't adapt to mouth tape or you want lower-risk entry — Intake is the right shape. Comfortable from night one, no sleep-apnea contraindication, makes nasal breathing easier without forcing it.