A fast and reliable range monitoring method is required to take full advantage of the high linear energy transfer provided by therapeutic ion beams like carbon and oxygen while minimizing damage to healthy tissue due to range uncertainties. Quasi-real-time range monitoring using in-beam positron emission tomography (PET) with therapeutic beams of positron-emitters of carbon and oxygen is a promising approach. The number of implanted ions and the time required for an unambiguous range verification are decisive factors for choosing a candidate isotope. An experimental study was performed at the FRS fragment-separator of GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany, to investigate the evolution of positron annihilation activity profiles during the implantation of 14 O and 15 O ion beams in a PMMA phantom. The positron activity profile was imaged by a dual-panel version of a Siemens Biograph mCT PET scanner. Results from a similar experiment using ion beams of carbon positron-emitters 11 C and 10 C performed at the same experimental setup were used for comparison. Owing to their shorter half-lives, the number of implanted ions required for a precise positron annihilation activity peak determination is lower for 10 C compared to 11 C and likewise for 14 O compared to 15 O, but their lower production cross-sections make it difficult to produce them at therapeutically relevant intensities. With a similar production cross-section and a 10 times shorter half-life than 11 C, 15 O provides a faster conclusive positron annihilation activity peak position determination for a lower number of implanted ions compared to 11 C. A figure of merit formulation was developed for the quantitative comparison of therapy-relevant positron-emitting beams in the context of quasi-real-time beam monitoring. In conclusion, this study demonstrates that among the positron emitters of carbon and oxygen, 15 O is the most feasible candidate for quasi-real-time range monitoring by in-beam PET that can be produced at therapeutically relevant intensities. Additionally, this study demonstrated that the in-flight production and separation method can produce beams of therapeutic quality, in terms of purity, energy, and energy spread.