In this work the abilities of intensity-modulated x-ray therapy (IMXT) and intensity-modulated proton therapy (IMPT) to deliver boosts based on theragnostic imaging were assessed. Theragnostic imaging is the use of functional or molecular imaging data for prescribing radiation dose distributions. Distal gradient tracking, an IMPT method designed for the delivery of non-uniform dose distributions, was assessed. Dose prescriptions for a hypoxic region in a head and neck squamous cell carcinoma patient were designed to either uniformly boost the region or redistribute the dose based on positron emission tomography (PET) images of the (61)Cu(II)-diacetyl-bis(N(4)-methylthiosemicarbazone) ((61)Cu-ATSM) hypoxia surrogate. Treatment plans for the prescriptions were created for four different delivery methods: IMXT delivered with step-and-shoot and with helical tomotherapy, and IMPT delivered with spot scanning and distal gradient tracking. IMXT and IMPT delivered comparable dose distributions within the boost region for both uniform and redistributed theragnostic boosts. Normal tissue integral dose was lower by a factor of up to 3 for IMPT relative to the IMXT. For all delivery methods, the mean dose to the nearby organs at risk changed by less than 2 Gy for redistributed versus uniform boosts. The distal gradient tracking method resulted in comparable plans to the spot scanning method while reducing the number of proton beam spots by a factor of over 3.