Research productivity is a common topic in the literature, but peer reviewing for journals has received less attention, although it is a key activity of academic research. We help to fill this knowledge gap by assessing the determinants of peer review engagement and quality in scientific journals. We do so by analysing the combined information from a survey of academics working in different parts of the world and various fields of science, along with their publication and peer review information gathered from Scopus and Publons/Web of Science. We find that age, gender, and some dimensions of academics' strategic research agendas are important predictors of peer review engagement. We also find that academic inbreeding along the educational path has a negative association with the quality of peer-review activities. However, we find no statistically significant results concerning academic inbreeding related to the professional trajectory and peer review engagement and quality. Equally importantly, our results suggest that although the activities of publishing and peer reviewing are closely associated, peer review tends to be ancillary to publishing, rather than the other way around. Furthermore, the greater the perceived availability of resources, including research funding throughout an academic's career, the greater the focus is on publishing and the less the focus is on peer reviewing. These findings are discussed in relation to the current valuation of publication versus peer reviewing in terms of scientific and academic career recognition.