Introduction: To capitalize on the increasing availability of accelerometry data for epidemiological research it is desirable to compare and/or pool data from surveys worldwide. This study aimed to establish whether free-living physical activity outcomes can be considered equivalent between three research-grade accelerometer brands worn on the dominant and non-dominant wrist. Of prime interest were the average acceleration (ACC) and the intensity gradient (IG). These two metrics describe the volume and intensity of the complete activity profile; further, they are comparable across populations making them ideal for comparing and/or pooling activity data. Methods: Forty-eight adults wore a GENEActiv, Axivity, and ActiGraph on both wrists for up to 7-days. Data were processed using open-source software (GGIR) to generate physical activity outcomes, including ACC and IG. Agreement was assessed using pairwise 95% equivalence tests (±10% equivalence zone) and intra-class correlation coefficients (ICC). Results: ACC was equivalent between brands when measured at the non-dominant wrist (ICC ≥ 0.93), but approximately 10% higher when measured at the dominant wrist (GENEActiv and Axivity only, ICC ≥ 0.83). The IG was equivalent irrespective of monitor brand or wrist (ICC ≥ 0.88). After adjusting ACC measured at the dominant wrist by −10% (GENEActiv and Axivity only), ACC was also within (or marginally outside) the 10% equivalence zone for all monitor pairings. Conclusion: If average acceleration is decreased by 10% for studies deploying monitors on the dominant wrist (GENEActiv and Axivity only), ACC and IG may be suitable for comparing and/or collating physical activity outcomes across accelerometer datasets, regardless of monitor brand and wrist.